Paul Hayes shot Scunthorpe into the Northern Area semi-finals of the LDV Vans Trophy with a silver goal at Gigg Lane.
Hayes was a second-half substitute as Iron boss Brian Laws surprisingly took off 17-goal marksman Steven MacLean.
And when presented with his chance in the eighth minute of extra time, Hayes showed as much composure as the on-loan star to settle a disjointed tie on a difficult icy surface.
"It wasn't inspiring football but to be honest who cares as long as we got through," said Laws after the match.
"It wasn't about how we played it was simply about getting through. It was a hard-fought match and it keeps our run going."
Scunthorpe are now unbeaten in 12 matches and hope to extend that run to 13 games in the Saturday's derby against Hull City.
In contrast, Bury have lost their last three matches and have failed to score in those three fixtures.
They only looked lively when Joe O'Neill came on as a second-half substitute for Chris Porter.
He had a couple of good opportunities that were saved by Tom Evans, while the lively and evergreen Peter Beagrie hit the post direct from a corner after 63 minutes.
"It was a disappointing way to go out," admitted Shakers player-boss Andy Preece.
"But we conceded the goal from one of our own free-kicks and that is becoming a bad habit.
"We kept Scunthorpe out for nearly 100 minutes against players like MacLean and Steve Torpey so that is one positive we can take out of this match."
