Charlie MacDonald opened the scoring from the penalty spot 15 minutes from time after the striker was judged to have been fouled by Rob Edwards.
And Sam Wood made the game safe three minutes later when he thumped the ball home from close range.
The Bees deserved the victory and could have won more comfortably had Exeter's Paul Jones not pulled off a string of fine saves throughout the game.
The Bees came close to opening the scoring midway through the first half when Dean Bowditch made a fine run and forced Paul Jones to save well with a strike from 15 yards.
On the half hour mark Marcus Stewart swapped passes with Steve Basham and struck the ball a yard past the post.
The visitors hit back and Kevin O'Connor then went close when his curling free kick from 25 yards was tipped over by Jones.
Exeter were again denied by Jones two minutes after the restart. Bowditch swapped passes with O'Conner and his close-range strike was superbly blocked by Jones.
Marvin Williams tested Jones again with a left foot shot from 12 yards but the City goalkeeper saved well to block the shot.
City substitute Craig McAllister almost scored with his first touch of the game when he met Matt Gill's cross and struck the ball narrowly wide.
MacDonald ran on to a long ball with 15 minutes left but Jones was quickly off his line to smother the ball.
But the game's decisive moment was just around the corner when Edwards was harshly judged to have fouled MacDonald and the striker picked himself up to stroke home the resulting penalty.