Richard Logan gave the Grecians a seventh-minute lead and although the home side dominated for most of the second half, they were unable to salvage a point.
Efe Sodje and Stephen Dawson were back for Bury after being left out of the midweek Johnstone's Paint Tropjy win over League One neighbours Stockport, meaning the Shakers had an unchanged line-up for the eighth straight league game.
The hosts had the first sight of goal as Andy Bishop's close-range shot was blocked by Matt Taylor, but the Grecians hit back to open the scoring moments later.
Jack Obersteller's left-wing cross was flicked on by Adam Stansfield and Logan got in behind David Buchanan to sidefoot the ball back across goal and inside the far post.
Mike Jones sent a tame header straight at Paul Jones in reply, while Buchanan volleyed narrowly wide from 20 yards.
Exeter midfielder Ryan Harley then tested Wayne Brown with a 25-yard drive, before Stansfield's low cross flashed across the face of goal.
Bury finished the half strongly, with Dawson firing over from Brian Barry-Murphy's clever corner, before keeper Jones had to turn Elliott Bennett's low strike wide.
The Shakers remained on top after the break with Bennett and Barry-Murphy testing Jones from long range, while Bishop had a strong penalty shout turned down.
Jones sliced a close-range effort off target as Bury continued to lay siege on the Grecians' goal, although Harley then fired narrowly wide after a rare Exeter attack.
Bury then made a double substitution with midfielder Richie Baker and striker Glynn Hurst coming into the fray and Jones did well to turn Bishop's 20-yard strike wide with 15 minutes left.
Bury substitutes Hurst and Baker went close late on, while Bishop fired agonisingly wide from ten yards.