Bury had the best of it before the break and Exeter had goalkeeper Paul Jones to thank for keeping his side in the game.
But after the break Exeter were the better side and could easily have grabbed a winner.
Bury should have gone ahead with only two minutes on the clock. Michael Jones fed Andy Bishop but the striker's close-range shot was tipped past the post by Jones.
At the other end, Adam Stansfield had shot well saved from a tight angle as Exeter attempted to impose themselves.
Andy Morrell thought he had put Bury ahead after swapping passes with Bishop but he was denied by the linesman's flag.
Bury were the better side in the first period. Elliot Bennett broke well down the right and picked out Michael Jones, but his shot flew over the bar.
Exeter attempted to strike on the break and Ryan Harley curled the ball narrowly over the bar from 25 yards.
Just before half-time, Bennett found Bishop who darted into the box and saw his shot well saved by Jones.
In added time, Manny Panther forced Mark Tyler to make a great safe with a shot from the edge of the box.
After the break, Richard Logan then tried his luck from 35 yards and his shot drifted just over the bar.
Harley also went close with a strike from edge of the box and Logan headed into the arms of the goalkeeper as Exeter pressed forward.
Stansfield struck a shot wide from a tight angle as the Grecians looked like opening the scoring.
As the second half wore on, Exeter dominated and Danny Seaborne headed into the arms of the goalkeeper.