Liam George scored his first goal in Bury colours as the Shakers kept up the pressure on the Nationwide Division Three promotion seekers.
George has been at Gigg Lane for more than three months but has not been able to command a regular first-team slot.
However, he had a fine match at Carlisle last week and followed it with an 82nd minute winner and a man of the match display.
The former Luton Town winger is set to see manager Andy Preece about a new deal on Monday.
And it will be hard for Preece to refuse after these three points move the Shakers into fifth place.
Centre half Steve Redmond is also now out of contract but he did enough in his 72-minute outing to deserve an extra deal.
Redmond eventually made way in a tactical switch for teenager David Nugent and it was the 17-year-old's assist that led to George's winner.
"It was a difficult decision who to take off," said Preece. "But Nuge is a massive talent for us and we had to get him on soon enough to make an impression.
"I always felt we would score but we had to be patient and stick to our game plan, even when the fans became a little restless.
"Liam has done well for us and now I can go to the board and show that he and Redders are making contributions.
"We will need a strong squad to get us out of this league and they are adding strength in depth." For Exeter, it was back to the drawing board after their midweek FA Cup win over Forest Green Rovers.
They have never beaten Bury in a league match at Gigg Lane but looked to be in with a shout of a point until George struck.
"I thought we'd done the hard work," said manager Neil McNab who will now step up his search for a striker.
"I felt we were going to see the game out and I can't criticise the lads because they gave me everything." Steve Flack missed a good chance to give Exeter a 68th minute lead but his close-range header flew wide. After that it was just a case of whether the Grecians could hold out under increasing pressure