- Manchester United needed the intervention of an ageing great to beat minnows Zorya as Zlatan Ibrahimovic, who turns 35 on Monday, headed home a second-half winner.
Inter Milan's aversion to Europa League football continued with a 3-1 defeat at Sparta Prague, while AS Roma ended a continental hoodoo stretching back seven games with a 4-0 home win over Romanian side FC Astra on Thursday.
The second round of group stage matches featured a string of high-scoring encounters as Fiorentina, Zenit St Petersburg and Krasnodar all hit five in comprehensive victories.
Yet while the goals flowed freely throughout the continent, Manchester United were made to sweat as they edged to a 1-0 win over Ukrainian outfit Zorya at Old Trafford.
It is six years since Inter last won the Champions League but they have not played in Europe's top club competition since 2012 and have now got a losing habit in its second-tier cousin.
They are already facing a difficult task to escape from their group after suffering a second straight defeat this season, which was their fourth in a row in the competition.
The three times European champions have made a good start to Serie A under new manager Frank de Boer but came into Thursday's encounter looking to rebound from a shock defeat in their opening Group K game at home to Israel's Hapoel Beer-Sheva.
Their hopes were hit within 25 minutes, however, as they fell two goals behind after a double strike by Vaclav Kadlec.
Rodrigo Palacio pulled one back in the 71st but any hopes of a recovery ended when Andrea Ranocchia was sent off four minutes later and Mario Holek restored the Czechs' two-goal advantage.
Inter's Serie A rivals Roma had no such problems with talismanic forward Francesco Totti continuing to defy the ageing process as he played a pivotal role in their comprehensive demolition of Astra two days after his 40th birthday.
Totti had a hand in three of Roma's goals, teeing up Kevin Strootman for the opener, rattling the crossbar with a free kick for Federico Fazio to net the rebound and playing a clever flick to release Mohamed Salah for Roma's fourth.
The only one he did not play a part in was a 47th-minute own goal by Astra's Fabicio as Roma ended a run of seven matches without a win in European fixtures.
Manchester United also needed the intervention of an ageing great to beat minnows Zorya as Zlatan Ibrahimovic, who turns 35 on Monday, headed home a second-half winner.
United manager Jose Mourinho had signalled his intentions by picking a strong side that also featured world record signing Paul Pogba, Juan Mata and Marcus Rashford.
He was rewarded with a third consecutive win in all competitions to lift the mood at the club after they had previously suffered three straight losses.
"One week, three defeats. One week, three victories," Mourinho said. "But I was not depressed by the defeats and I am not over the moon with three wins."
Ajax Amsterdam ended a run of five successive home draws in Europe as they beat Standard Liege 1-0 to join FC Krasnodar, Schalke 04, Shakhtar Donetsk, Zenit St Petersburg and APOEL Nicosia on maximum points from their opening two group games.
Krasnodar won 5-2 against Nice, with the visiting French side's Italian striker Mario Balotelli scoring his fifth goal in four games, while Schalke won 3-1 at home to Salzburg and Shakhtar defeated visitors Braga 2-0.
Zenit's Aleksandr Kokorin scored twice in a 5-0 thrashing of AZ Alkmaar, while APOEL sneaked a 1-0 win at Olympiakos Piraeus thanks to an early goal from Pieros Sotiriou.
Fiorentina brushed aside Qarabag 5-1 with Khouma Babacar and Mauro Zarate both scoring twice against the Azerbaijani side who played an hour with 10 men after Elvin Yunuszada was sent off.