Andy Bishop headed a 14th-minute opener and after a Matt Oakley own goal in the 48th minute, the Shakers closed out a thoroughly-deserved victory.
Bury started strongly and Giles Coke had a 20-yard drive blocked before David Amoo won a corner on the right.
And Bishop rose highest to meet Peter Sweeney's inswinger and power home his third goal of the season.
Both sides played a passing game, with Bury's fluid midfield causing problems, but Exeter should have levelled when Guillem Bauza hit a close-range effort too close to Bury's on-loan keeper Trevor Carson.
The hosts responded with Coke sparking a fine move which saw Joe Skarz find Mike Jones, who curled a 20-yard effort just past the far post.
Amoo then headed narrowly wide from another Sweeney corner but Bury earned the second goal they merited shortly after the break when Jones turned right-back Steve Tully and his cut-back was turned past his own keeper by Oakley.
Efe Sodje somehow managed to clear just three yards out to prevent Bauza pulling a goal back.
But Bury might have made their fourth win of the season even more emphatic as Exeter keeper Arthur Krysiak denied Coke from Sweeney's cut-back.
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Bury doing a good job to claw their back into a mid-table position. The last three results must have restored their battered confidence after the Lowe and Mozika exits and the subsequent string of losses. Have to say it looks like Barker has done a good job in getting the Shakers back on track. I had thought he was not experienced enough for the role and that he was on his way out, but I'm only too happy to end up eating my words.