The victory at the Dinamo Stadion allowed the Belarusian champions to open up a three-point lead at the top of Group F, with their goals coming from Alexander Pavlov, Vitaly Rodionov and Renan Bressan. Franck Ribery scored Bayern's consolation.
Hleb, who returned in the summer to the club where he began his career, played the full match and stressed the underdogs always fancied their chances of turning over the German giants.
He said: "It was a very difficult game for us, but we battled right to the end and we're delighted now. Of course it's a sensational result, but we believed we could do it before the match.
"We're taking each game as it comes, and now we face Valencia. But we'll go there trying to take all three points."
BATE have won both their group matches, having previously downed Lille 3-1 in France, while for Bayern the defeat ended their nine-match winning streak at the start of the season and leaves them on three points in the group.
Valencia won 2-1 against Lille with two goals from Jonas, while Chelsea, who were 4-0 winners at Nordsjaelland, head Group E after Juventus were surprisingly held to a 1-1 home draw against Shakhtar Donetsk.
It took a powerful strike from defender Leonardo Bonucci for Juventus to earn a point after Alex Teixeira had put the Ukrainians ahead.
In Group G, where Celtic beat Spartak Moscow, goals from Alexis Sanchez and Cesc Fabregas helped Barcelona maintain their winning start to the season after a 2-0 success 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, before Sergio Busquets was shown a straight red card two minutes from time.
In Group H, also featuring Manchester United and Cluj, 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.