The Shakers had the chance to climb above the visitors in mid-table but Byron Harrison gave them a 38th-minute lead.
Captain Mark Roberts doubled their lead in the 75th minute and although Andy Bishop replied three minutes later with his sixth of the season, Bury couldn't claim a late equaliser.
The Shakers named an unchanged line-up but Trevor Carson picked up a back inury in the warm-up so Cameron Belford started in goal for the first time in seven weeks.
With the visitors playing a high line, the Shakers were struggling to find space to play the passing football they produced in Tuesday night's 2-2 draw against Notts County.
However, Bury captain Steve Schumacher tested the Stevenage keeper with a long-range effort while striker Shaun Harrad dragged a close- range effort back across goal.
Stevenage were a threat from set-pieces and balls into the box and after Bury failed to deal with a right-wing cross, the ball fell between Efe Sodje and Mark Hughes for Harrison to sweep home.
Bury improved before the break with Peter Sweeney lashing a diagonal strike narrowly wide and after the interval, Bishop was denied by a block and then an offside flag after glancing in Mike Jones' cross.
But Belford then denied Robin Shroot and the visitors kept coming forward, with Roberts glancing a free header home from Shroot's inswinging cross, despite Bury's claims for offside.
Shane Byrne was immediately brought on for right-back Phil Picken and his long ball found fellow sub Lenell John-Lewis in the box.
He was bundled over by Lawrie Wilson, with Bishop side-footing the spot-kick into the bottom-right corner for his third goal in three games. And the closest they went to equalising was a Scott Laird header that drifted inches wide of his own goal.
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