In the other matches, AEK Athens were beaten 0-2 by Bayern Munich, Young Boys held Valencia 1, Ajax beat Benefica 1-0, Hoffenhiem and Lyon drew 3-3, while Roma were too good for CSK Moscow, winning 3-0.
An impressive Juventus beat Manchester United 1-0 at Old Trafford on Tuesday to take command of Champions League Group H with a maximum nine points from three games and demonstrate just how far Jose Mourinho's side are from Europe's elite.
Paulo Dybala's 17th minute goal, a simple conversion after a low cross from the right by former United favourite Cristiano Ronaldo, won the game but the dominant Italian champions could have won by a much more convincing margin.
United needed their Spanish keeper David de Gea to be in top form as he made a series of good saves, including an excellent effort to keep out a second-half strike from Ronaldo.
If United fans can see little hope of their side catching up the top trio in the Premier League they will also know after this game that there is precious chance of them doing better in continental action.
With four points leaving them second in their group, ahead of Valencia and Young Boys, United may still progress to the knockout stages but the gulf between them and a team equipped to reach the latter stages was all too evident.
United were unchanged from the team that drew at Chelsea in the Premier League on Saturday but the visitors very quickly demonstrated that they had no fear of the task in front of them.
Perhaps United's players would have been better joining their manager Jose Mourinho on the ten-minute walk from the team's hotel to the stadium than sitting in traffic for an hour on the team bus because they made a woefully slow start.
Right from the outset, Massimiliano Allegri's side were sharper, faster, more precise and showed more purpose than Mourinho's men, who struggled to even match the tempo of the Italian champions.
The most disconcerted Juve looked in the early exchanges was when a fan invaded the pitch only to be apprehended by security before he could reach his apparent target, Ronaldo.
It was no surprise at all when, in the 17th minute, Juve took the lead.
Ronaldo broke down the right and put in a low cross towards the near post which Chris Smalling and Juan Cuadrado challenged for before the ball fell kindly to Dybala, who converted with ease.
Juve sensed the fear in their opponents and looked for a quick second as Joao Cancelo burst unchallenged into the area and then tested United De Gea with a fierce drive.
It was a busy opening half for the Spanish keeper -- Ronaldo struck a swerving free-kick straight at De Gea, who then did well to keep out the follow-up effort from Blaise Matuidi.
The halftime statistics showed a remarkable dominance for a visiting side at Old Trafford with Juve enjoying 67 percent of possession and double the amount of passes.
Ronaldo, operating in a free role, roaming wide when he felt it would be fruitful, brought another fine save from De Gea seven minutes after the interval with a thundering shot after being set up by Cuadrado.
United's effort could not be faulted, however much guile and penetration they lacked, and they could have drawn level in the 75th minute when Paul Pogba, facing his former club, struck the post with a left foot shot from outside the box.
At the final whistle, another fan tried to greet Ronaldo and came up against security officers but the Portuguese insisted on taking a photograph with the interloper and left the field to the applause of both sets of fans.
Once again, United fans were left with a reminder of their glorious past in the shape of their old boy Ronaldo. It was their only consolation after a game in which their current weaknesses were so comprehensively exposed.
Real end winless run against Plzen
Real Madrid snapped a run of five games without victory by earning a 2-1 win at home to Viktoria Plzen in the Champions League on Tuesday yet were still booed off the pitch by their own supporters after an unconvincing performance.
Karim Benzema headed the stuttering triple European champions ahead early in the first half but they were fortunate not to concede an equaliser before the break as the Czechs somehow failed to capitalise on three clear opportunities.
Brazilian left back Marcelo got Real's second goal with a coolly-taken dinked finish in the 55th minute and they then missed a glut of chances to extend the lead, which was cut by an ice-cool finish from Plzen's Patrik Hrosovsky in the 78th.
Real held on for a far-from convincing win which keeps them level with Group G leaders AS Roma on six points after three games but failed to answer serious questions about their form ahead of Sunday's 'Clasico' away to arch rivals Barcelona.
A run of five games without a win culminating in Saturday's shock 2-1 home defeat by Levante had left Lopetegui against the ropes and he faced repeated questions about his precarious position in the build-up to the game.
The former Spain manager had insisted he felt able to continue at the helm in Madrid yet could still not give any guarantees that he would remain in charge by the weekend.
Benzema's headed goal from a superb cross by Lucas Vazquez brought a sense of calm to a nervy Santiago Bernabeu crowd although there were howling whistles at halftime after Real had given up a third chance to the Czechs but got away with it.
The visitors had missed an early opportunity when Milan Petrzela was denied at the near post by goalkeeper Keylor Navas and then managed to send the rebound wide.
David Limbersky failed to hit the target after getting past Lucas Vazquez and Hrosovsky then missed an even easier opening before the break when Navas flapped but the midfielder lacked composure and sent the ball over the bar.
Real's Uruguayan youngster Federico Valverde gave the home side a huge lift moments after coming off the bench to make his debut, winning possession and finding Gareth Bale whose backheel helped the ball to Marcelo who calmly converted.
Real captain Sergio Ramos came close to scoring as the hosts sought a third goal to wrap up the points but instead had to see the game out after Hrosovsky made amends for his earlier miss.
The final whistle provided little relief to the edgy home supporters, who let out a cacophony of boos and whistles despite Real winning for the first time in over a month.
City flex muscles with rampant win at Shakhtar
Manchester City began to show their credentials like proper Champions League heavyweights when they became the first English team to win at Shakhtar Donetsk in European competition with a handsome 3-0 success in their Group F match.
City, who false-started in the campaign with their only loss of the season at home to Olympique Lyonnais, were a wholly different proposition, waltzing to victory with goals from David Silva, Aymeric Laporte and substitute Bernardo Silva.
What looked a potentially difficult 1,700-mile visit to the Ukrainian champions, who had beaten Pep Guardiola's men in the group stages last year, was made to look effortlessly routine as the dazzling David Silva orchestrated their dominance.
City could easily have scored more goals but the win put the English champions top of the group on six points, a point clear of Lyon, who drew 3-3 at a Hoffenheim team who have two points along with bottom-placed Shakhtar.
City manager Pep Guardiola suggested on the eve of the match that the club may still lack the special passion for the competition that could drive them to European glory but his team of all talents demonstrated they certainly have the quality.
Shakhtar had never been beaten by English visitors in seven home matches, leaving Guardiola to appreciate the magnitude of the win. "Zero-three here," he said, "It's an amazing result.
"We've recovered with these two results in Germany (a win at Hoffenheim) and here. After the defeat against Lyon, it's in our hands again and winning our games at home will be the next stage."
The English Premier League leaders, with Kevin De Bruyne back for his first full start of the season after an injury layoff, continued their recent dazzling form by taking control from the opening whistle.
In the first half hour, Riyad Mahrez could and maybe should have scored twice, once after City had broken with breathtaking pace from their own half before he then also set up David Silva to flick the ball impudently against Shakhtar's post.
Yet the Spanish maestro made no mistake with a left foot volley just after the half-hour to reward City's mastery.
Five minutes later, De Bruyne's corner fell to Laporte, who found himself unmarked as he stooped to head home.
Though the home side attacked intermittently, City could have scored three more goals in the space of the first 12 minutes of the second half as they continued to pour forward.
Bernardo Silva had been on the pitch for 90 seconds after the excellent De Bruyne's withdrawal when another devastating City counter saw the Portuguese midfielder race through and slot his 71st minute left-foot shot in off the far post.
It sealed Shakhtar's first defeat in 12 matches in all competitions, leaving their chances of qualifying for the knockout stages looking bleak.
Dzeko the destroyer as Roma home joy continues
AS Roma's Edin Dzeko drew level with Barcelona's Lionel Messi at the top of this season's Champions League scoring charts as the Italians set the pace in Group G with a 3-0 win over CSKA Moscow at the Stadio Olimpico.
The Bosnia-Herzegovina striker netted twice in the first half to take his tally in the competition to five goals, before setting up Cengiz Under to score the third just after the break as Roma continued a strong run of home form in Europe.
Eusebio di Francesco’s side were unbeaten in Rome during their run to the semi-finals last season and have not suffered a home defeat in European competition since a 1-0 Europa League loss to Villarreal in February 2017.
The result leaves Roma top of the section level on six points with Real Madrid, two ahead of CSKA and five clear of Viktoria Plzen, who lost 2-1 to the European champions in Spain.
The Russian side had a night to forget on their last visit to the Italian capital in 2014, losing 5-1, and endured another difficult night as Roma recorded a seventh straight Champions League home win ahead of the visit of Real Madrid on Nov. 27.
The Italians took the lead after half an hour when Lorenzo Pellegrini’s neat passing exchange with Stephan El Shaarawy found him some space inside the area and Dzeko was on hand to tap in the midfielder’s low cross from close range.
Roma doubled their lead two minutes before the break and Pellegrini was again at the heart of the move, surging through the CSKA defence before El Shaarawy picked out the Bosnian, who showed good composure to finish from a tight angle.
Dzeko was again involved as the hosts added a third five minutes after the restart, rising to nod a long ball into the path of the onrushing Under, who applied a powerful finish.
Quick double strike gives Bayern 2-0 win at AEK
Bayern Munich scored twice in two minutes to beat hosts AEK Athens 2-0 to continue their recovery from a recent dip in form and climb to the top of their Champions League Group E.
Javi Martinez volleyed in after 61 minutes and Robert Lewandowski tapped in their second goal two minutes later for their second win in three group matches.
The result gave the Bavarians a further shot of confidence after Saturday's league win at VfL Wolfsburg ended a four-game winless run in all competitions, and silenced any talk of a crisis.
The Greek champions did it well for about an hour but ultimately could not match Bayern's speed and power.
Bayern were in control of an entertaining first half, with Serge Gnabry and forward Lewandowski coming close several times.
AEK, who have yet to earn a point after three matches, carved out a couple of scoring chances as they caught the Bavarians off guard, with Ezequiel Ponce thundering a powerful shot narrowly wide.
The hosts piled on further pressure after the break, pressing high and coming close with Viktor Klonaridis before Martinez' acrobatic volley silenced the crowd at the Olympic Stadium.
Bayern, who have never lost to a Greek club, home or away, quickly killed off the game two minutes later, with Lewandowski left with too much space in front of goal to slot it a Rafinha cutback.
Bayern are on seven points from three games, with Ajax Amsterdam, who take on Benfica later on Tuesday, on four. Benfica are on three.