Byron Harrison and Mark Roberts both scored to end the Shakers' three-game unbeaten run at Gigg Lane.
Neither team had looked likely to score until Stevenage struck seven minutes before the break. The ball broke for Harrison inside the box and he clipped a neat finish into the corner of the net.
The Shakers had a strong penalty appeal turned down when Ronnie Henry appeared to trip Giles Coke, while Shakers' striker Andy Bishop had a goal ruled out for offside, but Stevenage extended their advantage, Roberts springing the offside trap to head home a cross from Joel Byrom.
Bury finally got their goal when Lenell John-Lewis was brought down by Lawrie Wilson inside the penalty area and Bishop scored from the spot.
Stevenage had the better of the closing stages as they sealed back-to-back away wins, although Scott Laird narrowly avoided heading into his own net.
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