SECOND-half goals from Chris Hussey and Tom Soares secured a third successive win for Bury and moved them up to within seven points of the League Two play-off positions.
Hussey curled a 25-yard free kick into the bottom corner to open the scoring in the 65th minute, seemingly catching Grecians keeper Artur Krysiak off guard as he prepared for a cross.
Exeter were then reduced to 10 men on 69 minutes after centre-back Danny Coles picked up a second yellow card in the space of five minutes.
And Soares came off the bench to score his second goal in as many games, poking home from close range in the second minute of stoppage time.
The victory, which moved Bury up to 11th place in the table, extended their unbeaten home run to 13 matches and came on the back of their 10th clean sheet in the last 18 games.