Arsenal have suffered a shock 2-1 loss to Dinamo Zagreb, after they were reduced to 10 men on 40 minutes, when striker Olivier Giroud was sent off.
Chelsea put their poor Premier League form behind them to record a 4-0 win over Maccabi Tel Aviv, while Bayern Munich beat Olympiakos 3-0.
Roma held Barcelona to a 1-1 draw thanks to a stunning strike from halfway from Alessandro Florenzi.
Results:
Group E
Bayer Leverkusen (Mehmedi 4', Calhanoglu 47', 75', Hernandez 59') 4 - 1 BATE Borisov (Milunovic 13')
Roma (Florenzi 31') 1- 1 Barcelona (Suarez 21')
Group F
Dinamo Zagrab (Pivaric 24', Fernandes 58') 2 - 1 Arsenal (Walcott 79')
Olympicakos 0 - 3 Bayern Munich (Muller 52', 90', Goetze 89')
Group G
Chelsea (Willian 15', Oscar 45', Diego Costa 59', Fabregas 79') 4 - 0 Maccabi Tel Aviv
Dynamo Kyiv (Gusev 20', Buyalsky 89') 2 - 2 FC Porto (Aboubakar 23', 81')
Group H
Gent (Milicevic 68') 1 - 1 Lyon (Jallet 58')
Valencia (Cancelo 55', Gomes 73') 2 - 3 Zenit St. Petersburg (Hulk 9', 45', Witsel 76')