Barcelona came from behind to beat Bayer Leverkusen 2-1, while Bayern Munich thrashed Dinamo Zagreb 5-0 in Tuesday’s Champions League action.
The hosts raced into a 3-0 lead with just half an hour gone thanks to an early goal from Ihar Stasevich and Filip Mladenovic’s double.
Gervinho and Vassilis Torosidis pulled goals back in the second half but BATE held on for a famous win.
Barcelona averted another upset with two late goals to some from behind and beat Bayer Leverkusen 2-1.
Kyriakos Papadopoulos headed the Germans into a 21st-minute lead and Barca, without talisman Lionel Messi through injury, struggled to get back into the game.
But Carnicer Sergi Roberto eventually equalised in the 81st minute and 90 seconds later Luis Suarez secured three points for the off-colour Catalan giants.
Less of a surprise was Robert Lewandowski being back among the goals, the striker taking his personal tally to 10 in three games with a hat-trick as Group F leaders Bayern Munich thumped Dinamo Zagreb 5-0.
In Chelsea’s group, goals from Andriy Yarmolenko and Aluisio Junior Moraes gave Dynamo Kiev a 2-0 victory over Maccabi Tel-Aviv while in Group H, Valencia won 1-0 in Lyon and Zenit St Petersburg beat Gent 2-1.