Messi opened the scoring after two minutes and eight seconds, the quickest goal of his career, slipping the ball through Thibaut Courtois' legs from a tight angle.
Cristiano Ronaldo scored twice in his 150th European appearance to give Real Madrid a 3-1 victory at Borussia Dortmund, their first against them in Germany, and make it two wins out of two matches in their Champions League Group H.
The Chelsea coach said his side's win over Besiktas had been a great test of character in the face of a hostile crowd.
A summary of Tuesday's group matches in the UEFA Champions League.
Images from the Europa League matches played on Thursday
Turkey plans to host the Champions League final in August, the head of its football federation said on Wednesday, after it was postponed by the global coronavirus pandemic. Two months ago European soccer's governing body UEFA indefinitely postponed the final, which had been scheduled to be played in Istanbul in May.
Tottenham Hotspur's Erik Lamela scored a stunning 'rabona' goal to light up Thursday's Europa League ties, wrapping his left boot round the back of his right leg 20 metres out and blasting the ball into the top corner.
Images from Champions League matches played across Europe on Tuesday
Bastia game abandoned after fans attack Lyon players
A leading Turkish soccer club have banned their players from growing beards after their chairman said they looked like students of Islamic vocational schools and set a bad example.
Arsenal qualified for a 17th successive season with a nervy 1-0 win at home to Besiktas and Malmo made it for the first time with a 3-0 win over Salzburg, whose participation ended in the qualifiers for the ninth time in a row.
Manchester United's new winger Angel Di Maria will not change the course of their troubled season straight away following his British record transfer from Real Madrid, manager Louis van Gaal said on Tuesday.
Turkish side Fenerbahce will be unable to compete in the Europa League this season after the Court of Arbitration for Sport (CAS) upheld a UEFA-imposed two-year ban from European competition over a match-fixing scandal on Wednesday.
News of all that's transpired on and off the football field
Manchester United's misfit striker Bebe has moved to Portuguese side Rio Ave on loan in a bid to resurrect his career at home.
Robert Lewandowski scored a brilliant free kick to give Bayern Munich a 1-0 win over Atletico Madrid in their last Champions League Group D outing on Tuesday, ending the 100 percent record of their opponents. The Poland international curled the ball over the wall and into the corner of the net in the 28th minute but the goal had no impact on the final standings with Atletico guaranteed top spot and Bayern in second place.
Among other transfer news globally, defender Rahul Bheke joins Mumbai City FC while Locatelli completes Juventus move.
Napoli's Marek Hamsik enjoyed a memorable return to his former club Slovan Bratislava, scoring one and creating another, in a 2-0 victory on Thursday as the Italians joined five others who made it two wins from two in the Europa League group stage.
Champions League records from 1992-2010 ahead of the 2010-2011 season.
Liverpool, Paris St Germain, Besiktas, Dynamo Kiev, Sparta Prague and Villarreal reached the knockout stages of the Europa League on Thursday in contrasting fashions.
Last month, Fonseca vowed that he would don the iconic masked vigilante's outfit if the Ukranian side progressed to the last 16 and stuck to his word, wearing a black cape, mask and hat during the post-match presser after the win.
Any sliver of a doubt over whether Cristiano Ronaldo would lead Portugal into the Euro 2016 was erased on Tuesday when he was named in their 23-man squad for the finals.
Manchester United manager Alex Ferguson begins another Champions League campaign at Besiktas on Tuesday confident his team will not repeat the mistakes which forced them to lose last season's final against Barcelona.
Didier Drogba scored twice on his return from a three-match European suspension as Chelsea drew 2-2 at Atletico Madrid to seal their place in the knock-out round of the Champions League on Tuesday. They were joined in the last 16 by Manchester United, Porto and Girondins Bordeaux, although four-time European champions Bayern Munich are on the brink of elimination after losing at home to the French champions.
Winger Marco Reus was left out of World Cup winners Germany's final Euro 2016 squad on Tuesday over injury concerns, coach Joachim Loew said.
Schalke 04 hit back from two goals down to draw 2-2 and overcome fellow Germans Borussia Moenchenglach on away goals in their Europa League last 16 tie while Manchester United edged Rostov 1-0 to progress on Thursday.
News of all that's transpired on and off the football field
The fixtures for the group stages in the 2009-10 UEFA Champions League, which kicks-off on Wednesday.
Liverpool continued their revival with a 4-1 home win over Porto while Real Madrid lost 2-3 at Werder Bremen in Wednesday night's Champions League matches.
Arsenal are on a roll having won their last 12 matches in all competitions, while Liverpool smarting from a defeat in the Champions League.
Manchester United manager Jose Mourinho said Friday's draw for the last 16 of the Europa League against Russian side Rostov has been unkind to his team, the favourites.
Liverpool scored twice in the last nine minutes to beat Fulham 2-0 to move up to fourth in the Premier League on Saturday.
The Liverpool manager hailed his rejuvenated team after they recorded the Champions League's biggest win by hammering Besiktas 8-0.
Israel international Yossi Benayoun scored a hat-trick as the 2005 champions and runners-up last season overwhelmed Besiktas in the Champions League on Tuesday.
The 2005 champions and last season's runners-up take on Besiktas in a must-win match on Tuesday knowing that even if they win their remaining three Group A games they could still fail to get through.
Striker Robinho scored twice in a virtuoso second-half display to help Real Madrid to a 4-2 victory over 10-man Olympiakos in an action-packed Champions League game at the Bernabeu on Wednesday.
Leverkusen finally subdued Besiktas with two goals in the last 13 minutes to secure the 2-1 win they needed to overhaul their Turkish opponents for third place in Group B.
Arsenal teenager Bukayo Saka scored his first goal for the club as they beat 10-man Eintracht Frankfurt 3-0, while Manchester United's 17-year-old Mason Greenwood secured a 1-0 win over FC Astana as the Europa League group stage began on Thursday.
The 31-year-old is still recovering from the knee injury which forced him to limp out of the Euro 2016 final against France in the first half, coach Fernando Santos said.