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Shakhtar could have gone through with a win but lost 3-2 at stuttering holders Chelsea, who netted in injury time through Victor Moses's header.
Juventus powered to 4-0 home victory over Denmark's Nordsjaelland but the Turin side stay in third place.
Peruvian striker Claudio Pizarro bagged a 15-minute first-half hat-trick to help hosts Bayern batter Lille 6-1 and top Group F.
Valencia were 4-2 victors at home to BATE Borisov thanks to Sofiane Feghouli's brace.
Substitute Oscar Cardozo scored twice and missed a penalty as Benfica beat 10-man Spartak Moscow 2-0 in Lisbon.
Favourites Barca lost 2-1 in Glasgow after Victor Wanyama and Tony Watt struck in a famous win for the modest yet non-stop Scottish champions.
Manchester United came from behind to win 3-1 at Braga after Robin van Persie, Wayne Rooney and Javier Hernandez sealed a knockout stage berth as group winners.
Galatasaray's 3-1 win thanks to Burak Yilmaz's perfect hat-trick in Cluj left second spot in Group H wide open.