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.
Bayern manager Jupp Heynckes could only appreciate the physical effort which went into BATE's glory night.
He said according to fcb.de: "I knew before the match we were up against very good opponents. They're extremely well organised, especially in defence, and they proved that again.
"But more than anything else, they fought till they dropped, especially when we applied pressure. In a game like that, you have to take the lead, but if you don't, your opponents can counter-attack from a defensive platform.
"They did that very well. But our opponents' best player was their goalkeeper, and from that you can see we applied pressure the whole time. But at the end of the day, you have to applaud our opponents for winning."