Goals Alexander Pavlov and Vitaly Rodionov put the Belarusian champions in charge and although Bayern pulled one back in stoppage time through Franck Ribery, BATE added a third through Renan Bressan to seal their first ever home win in the competition.
The victory means unfancied BATE have now won both their group matches having previously downed Lille 3-1 away, while for Bayern the defeat ends their nine-match winning streak at the start of the season and leaves them on three points in Group F.
Valencia got their Champions League campaign up and running as two goals from Jonas sealed a 2-0 win over Lille.
Champions League holders Chelsea claimed their first win of this year's competition after seeing off Nordsjaelland 4-0 in Group E.
Roberto Di Matteo's men were made to work hard for their triumph at the Parken Stadium in Copenhagen, and they only sealed victory with three goals in the last 11 minutes as their Danish opponents ran out of steam.
Juan Mata notched his third goal in as many games and added the third after a superb free-kick from David Luiz before Ramires completed the scoring.
They now top the group after Juventus were surprisingly held to a 1-1 home draw against Shakhtar Donetsk.
It took a thunderbolt from defender Leonardo Bonucci to guarantee a share of the spoils after Alex Teixeira had put the Ukrainians ahead on the counter-attack.
Georgios Samaras' late header earned Celtic a 3-2 Group G victory over 10-man Spartak Moscow in the Luzhniki Stadium.
Striker Gary Hooper gave the visitors the lead in the 12th minute before Emmanuel Emenike netted either side of the break, but after Spartak defender Juan Insaurralde was sent off, the tide changed in Celtic's favour.
They levelled in the 72nd minute when substitute James Forrest's strike deflected off Dmitri Kombarov and Samaras capped a remarkable night for the Hoops after heading in Emilio Izaguirre's cross seconds after the regulation 90 minutes.
Goals either side of half-time by Alexis Sanchez and Cesc Fabregas helped Barcelona maintain their perfect start to the season after a 2-0 win at Benfica.
However, the Catalans' night was soured towards the end when captain Carles Puyol was carried off on a stretcher with what appeared to be a broken arm after he landed awkwardly when attacking a corner, before Sergio Busquets was shown a straight red card two minutes from time.
In Group H, Robin van Persie scored his first Champions League goals for Manchester United, who came from behind to beat CFR Cluj 2-1.
Pantelis Kapetanos had put the Romanian champions in front in the 14th minute but United went three points clear at the top thanks to Van Persie's strikes either side of the interval.
Galatasary were made to pay for poor finishing as a 27th-minute goal from Ruben Micael and a last-gasp effort from Alan gave Braga a smash-and-grab 2-0 win.
Tuesday's UEFA Champions League Results