Joey Barton scored directly from a corner as Marseille drew 2-2 with Europa League Group C rivals Borussia Monchengladbach.
Uruguay striker Edinson Cavani netted all four goals as Napoli ended Dnipro's 100% winning record with a 4-2 win.
Defending champions Atletico Madrid's perfect start was ended by Academica, while Lyon's fourth straight win puts them into the knockout stages.
Group H pair Inter Milan and Rubin Kazan progressed with victories.
Bayer Leverkusen, Hannover and Metalist Kharkiv also booked their places in the knockout phase with victories on matchday four.
Following Thursday's fixtures, there are two rounds of matches remaining before the competition enters the last 32 stage with the addition of eight teams dropping down from the Champions League.
Ex-England midfielder Barton, on-loan from Queens Park Rangers, drew Marseille level in their important Group C tie against visitors Monchengladbach, who had led through Mike Hanke's first-half opener.
Jordan Ayew put the French hosts ahead before Juan Arango's added-time goal left the sides tied on five points each, five adrift of leaders Fenerbahce. The Turkish side won 2-0 against AEL Limassol.
Dnipro still look favourites to progress from Group F, despite Cavani dashing their hopes of sealing early qualification. The Ukrainians led 2-1 before three goals in the final 13 minutes prevented Napoli from suffering their first loss in 16 continental home games.
Wilson Eduardo's brace helped Portuguese side Academica clinch their first European victory since 1969 and kept alive their slim hopes of advancing from Group B. The 2-0 win also ended Atletico Madrid's 16-match winning run in continental competition.
Goals from Bafetimbi Gomis and Yoann Gourcuff put Group I leaders Lyon in a commanding position at last season's beaten finalists Athletic Bilbao. But Athletic drew level through Ander Herrera and Aritz Aduriz before Alexandre Lacazette's 63rd-minute strike assured the French side's place in the round of 32.
2010 Champions League winners Inter Milan and Russian rivals Rubin Kazan both knew victories would secure their early passages from Group H. Two goals from Rodrigo Palacio and another from Fredy Guarin helped Inter beat Partizan Belgrade 3-1, while Vladimir Dyadyun earned Kazan a narrow 1-0 win at Azerbaijani hosts Neftci.
Swiss side Young Boys moved alongside second-placed Liverpool on six points in Group A following their 3-2 win at Udinese. Udinese's talisman Antonio Di Natale cancelled out Raul Bobadilla's opener before Alexander Farnerud and Raphael Nuzzolo put the visitors in command. Diego Fabbrini's late strike was merely a consolation for the Italians.
Newcastle's Group D rivals Bordeaux beat Maritimo 1-0 thanks to a goal from ex-Sunderland and Manchester United striker David Bellion. The French side are one point behind leaders Newcastle and three ahead of third-placed Club Bruges with two games remaining.
Lazio consolidated their place at the top of Tottenham's Group J with a comfortable 3-0 success against Greek visitors Panathinaikos in Rome. Czech striker Libor Kozak scored twice with Sergio Floccari adding the other.