Captain Kostas Fortounis scored late from the penalty spot to help Olympiakos defeat AC Milan 3-1 on Thursday and knock the seven-time European champion out of the Europa League.
Sevilla, Villarreal, Genk, Celtic, Rapid Vienna, Malmo, Krasnodar, Rennes, BATE and Slavia Prague also qualified for the knockout rounds of Europe's second-tier competition on the final night of group-stage matches.
The five-time winner of the competition, Sevilla advanced from Group J after a 3-0 win over Krasnodar, which also advanced. Villarreal defeated Spartak Moscow 2-0 to progress from Group G with Rapid, which scored in the 84th minute to win 1-0 and knock out Rangers.
In Group B, Celtic avoided elimination despite a 2-1 defeat at home to Salzburg after Leipzig drew with Rosenborg 1-1.
Genk cruised to the next phase with a 4-0 rout of Sarpsborg in Group I, and Malmo also made it with a 1-0 away victory over Besiktas.
Rennes' new coach, Julien Stephan, celebrated a 2-0 victory in Group K and a spot in the next round by knocking out Astana, and Slavia Prague made it with a 2-0 win over Zenit in Group C.
Arsenal, Bayer Leverkusen, Chelsea, Dinamo Zagreb, Dynamo Kiev, Eintracht Frankfurt, Fenerbahce, Lazio, Real Betis, Salzburg, Sporting, Zenit and Zurich already booked their places in the round of 32 earlier in the competition.
Eight teams knocked out of the Champions League — Benfica, Club Brugge, Galatasaray, Inter Milan, Napoli, Shakhtar Donetsk, Valencia and Viktoria Plzen — also qualified for the round of 32 by finishing in third in their groups.
The draw for the round of 32 will be held on Monday, an hour after the Champions League draw is held.
Although Chelsea failed to keep a perfect group-stage record, Willian and Olivier Giroud salvaged a 2-2 draw against Vidi in Budapest by scoring from free kicks.
But the game was marred by Chelsea supporters singing an anti-Semitic chant, with the club condemning their behavior in a statement and saying it has no place at Chelsea. The incident came just days after four fans were suspended for abusing Manchester City forward Raheem Sterling.
In London, Arsenal celebrated captain Laurent Koscielny's return from a torn Achilles tendon with Alexandre Lacazette scoring in a 1-0 win against Qarabag.