The Belarusians won their opener against Lille and followed that up with a famous victory in their own stadium in Minsk.
It was the first defeat after nine straight wins in all competitions for German league leaders Bayern and they were always on the back foot once Aleksandr Pavlov put the home side ahead after 23 minutes.
Vitali Rodionov doubled the lead with 12 minutes remaining before Franck Ribery first struck the post then grabbed a 90th minute lifeline for the visitors.
Brazilian Renan Bressan sealed a famous victory for BATE with a clinching third on the counter attack in the fifth minute of injury time.
"This is a sensational result for us, we will celebrate a bit but we need to keep working hard," BATE's ex-Arsenal star Aleksandr Hleb told AFP.
"Bayern are still favorites in our group, we are taking it one match at a time.
In the other match in Group F, Valencia condemned Lille to their second straight defeat with a 2-0 win at the Mestalla in Spain.
Goals from Jonas in either half clinched the vital win for Valencia.
An upset also looked possible when Manchester United trailed to minnows CFR Cluj in Romania through an early strike from Pantelis Kapetanos.
But a pair of goals from Robin van Persie, both time assisted by Wayne Rooney, secured victory for Alex Ferguson's men.
They top Group H with two wins, while FC Braga beat Galatasaray 2-0 in the other match played.
Reigning champions Chelsea secured their first victory in Group E, beating Danish minnows FC Nordsjaelland 4-0 in Copenhagen.
A Juan Mata goal just before half time was all that separated the two sides for much of the encounter and Chelsea goalkeeper Petr Cech made a superb save to touch a Joshua John shot on to the post after the break.
But David Luiz rifled home a second from a free kick, Mata scored his second, and Ramires with the fourth put a gloss on the scoreline.
Juventus, who held Chelsea at Stamford Bridge in their opener, had to come from behind to salvage a point against Shakhtar Donetsk in a 1-1 draw in Turin.
Willian fed fellow Brazilian Alex Texeira to fire the Ukrainians ahead after 23 minutes.
But Serie A champions Juventus preserved their 45-match unbeaten run when Leonardo Bonucci scored from Andrea Pirlo's corner just a minute later.
Barcelona won the heavyweight clash in Benfica 2-0 to maintain their 100 per cent start to Group G.
Alexis Sanchez put Barca ahead after only six minutes and midfielder Cesc Fabregas sealed three points in the Stadium of Light after the break.
Their night was partially spoilt with two minutes to go when Sergio Busquets was shown red after a clash with Maxi Pereira.
Scottish champions Celtic are giving chase on four points after a 3-2 away win over Spartak Moscow.
Celtic went into the match in the Russian capital with a record of 11 straight losses on the road in the Champions League and 21 games without a win away from home.
But an early goal from Gary Hooper gave Neil Lennon's men great encouragement.
Spartak hit back to lead 2-1 after an Emmanuel Emmenike double, but home defender Juan Insaurralde was sent off just after the hour mark for pulling back Hooper.
Celtic leveled when substitute James Forrest's shot found its way home via a rebound from defender Dmitri Kombarov.
Giorgos Samaras headed a dramatic and deserved late winner for Celtic.