The English club, last season's Europa League winners, went into the continental tie having not registered a goal in their first three Premier League fixtures of the campaign.
Villa captain John McGinn gave his team the lead after just 11 minutes, expertly side-footing a first-time shot into the bottom left corner after being set up by Pau Torres' driving run out of defence.
The home side found the equaliser in the 19th minute when Hugo Vetlesen found the back of the net but Emiliano Buendia restored the English side's lead just three minutes later.
Villa then scored a third goal in a breathless first half as striker Nicolas Jackson ran in behind to try and latch onto Torres' long ball, beating goalkeeper Yann Sommer to the ball and slotting into an empty net for his first goal since joining in a club-record £65m move.
Brugge pulled one back just after the hour mark through Nicolo Tresoldi's penalty, awarded for handball on Aaron Wan-Bissaka after the referee was sent to the VAR monitor.
Villa had to withstand a heavy onslaught from the home team in the closing stages but held on for what would no doubt be a morale-boosting victory.
Nicolas Jackson scored twice as Aston Villa beat Manchester City 2-1 to end the visitors' perfect start to the Premier League season. The victory also extended Villa's unbeaten run in all competitions to seven matches.
Bayern Munich expect coach Vincent Kompany to be sidelined for weeks rather than days after collapsing at the training ground with a virus, sporting director Max Eberl has confirmed.
Erling Haaland will be available for Manchester City's Premier League trip to Aston Villa on Saturday after recovering from the knock that ruled him out of their 5-1 Champions League victory over AEK Athens.
Bayern Munich coach Vincent Kompany has backed Lennart Karl to rediscover his best form, insisting he is not worried about the teenager's recent struggles.
