Milan was held 0-0 by Glasgow Celtic but finished top of Group F, while Shakhtar Donetsk produced the surprise of the evening, a 2-0 victory over Spanish league leader Barcelona with two first-half strikes by Nigerian forward Julius Aghahowa.
Another Nigerian striker, Obafemi Martins, scored two as Inter Milan beat last-placed Anderlecht 3-0 to finish top of Group G ahead of Bremen.
On Wednesday, nine-time winner Real Madrid has to beat AS Roma in Rome's Olympic Stadium to reach the last 16. The game takes place in an empty stadium because UEFA has banned fans from Roma's home games after a referee was hit on the head with an object from the stands.
Leader Dynamo Kiev goes to Bayer Leverkusen in the other Group B game.
Four-time winner Liverpool has to beat Group A leader Olympiakos, while second-placed Monaco, last season's Champions League runner-up, hopes to avoid defeat at Deportivo de La Coruna, which is already out.
Juventus and Bayern Munich already have qualified from Group C and Manchester United and Lyon are through from Group D.