A brace from Amad Diallo gave United their first success in this season's competition, coming under interim manager Ruud van Nistelrooy after they had drawn the previous three games with Erik ten Hag was in charge.
Tottenham Hotspur made it three wins from three in the Europa League with a 1-0 win at home to AZ on Thursday but Manchester United remain winless after being held to a 1-1 draw at red-carded Jose Mourinho's Fenerbahce.
Manchester United manager Erik ten Hag has highlighted a lack of goals as the major factor behind the English giants' faltering start to the season.
Manchester United manager Erik ten Hag said his side had failed to maintain their intensity in Wednesday's 1-1 Europa League draw with FC Twente and should have pushed to kill the visitors off before they had the chance to equalise.
Erik ten Hag made a convincing case to be spared the sack as Manchester United upset Manchester City to take the FA Cup with a shock 2-1 victory in Saturday's final.
Leverkusen - or 'Neverlusen' as they had been dubbed after obliterating Bayern Munich's 11-year Bundesliga title monopoly in Germany - can still win a domestic double with victory against second-tier Kaiserslautern in Saturday's German Cup final.
Gian Piero Gasperini lavished praise on his "incredible" Atalanta players after they stunned Bayer Leverkusen to win the Europa League and claim their first ever continental honour.
Ademola Lookman scored a stunning hattrick as Atalanta ended Bayer Leverkusen's 51-match unbeaten run to win the Europa League final 3-0 on Wednesday and claim their first trophy for 61 years.
Bayer Leverkusen had won only two major trophies in their 119-year history before this season but on Wednesday the newly-crowned Bundesliga champions have the chance to claim a double when they face Atalanta in the Europa League final in Dublin.
"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
Atalanta knocked out Portuguese side Sporting Lisbon in the previous round but have won just two of their last nine matches in all competitions.
Leverkusen head into Thursday's home first leg against West Ham in the Europa League quarter-finals unbeaten in 41 matches this season, with 36 wins and five draws.
Jurgen Klopp's Liverpool, who are still in contention to win a quadruple this season, will entertain Atalanta at Anfield on April 11 and go to Italy a week later for the return.
AC Milan, Marseille, Roma and West Ham were among the other sides to also book their place in Friday's quarter-final draw.
Liverpool remain on course to send Jurgen Klopp off with a quadruple.
Mohamed Salah has given Liverpool a major boost after the Egypt star travelled to Sparta Prague for Thursday's Europa League clash following his recent injury lay-off.
AC Milan, meanwhile, were drawn against French club Rennes.
A youthful Liverpool side lost 2-1 at Union Saint-Gilloise in their final Europa League group game on Thursday, while Villarreal snatched a place in the last 16 from Rennes with a dramatic victory in France.
Jurgen Klopp's side sealed top spot in Group E thanks to Gakpo's brace and goals from Luis Diaz and Mohamed Salah at Anfield.