Nigel Adkins saw his Bramall Lane unbeaten start come to an end on Saturday.
With all the goals coming in the second half, Bury's professional display earned them the points.
Billy Sharp scored in a third successive league game but it was not enough to prevent the Blades losing in the league for the first time since the opening day of the campaign.
Illness ruled Adams out of the Sky Bet League One clash. Boss Adkins reverted to the team that beat Swindon with the exception of Woolford, taking over from Adams. Flynn and Scougall returned to the bench.
Despite Tutte firing weakly wide for Bury, the Blades made the brighter start, working hard to break down the visiting side's organised unit. Campbell-Ryce delivered a perfect cross which saw Sammon head straight at goalkeeper Lainton, who was well placed to hold Sharp's shot on the turn on 18 minutes.
The Blades continued to attempt to push Bury back with Woolford and Campbell-Ryce seeing plenty of the ball, whilst Reed curled a free-kick over the angle of post and crossbar following a foul on McEveley. Another Reed shot on 34 minutes was also wide.
As half-time approached referee Webb angered the home fans. He failed to show Soares a yellow card following a foul on Campbell-Ryce, which would have been the Bury midfielder's second, and then McEveley was booked when he won the ball close to the technical area.
Late in the half the Blades continued to be on the front foot and Bury's stalling tactics were evident even before the half-time whistle.
There was a frantic start to the second half as United looked to up the tempo and there were two early chances. From Edgar's chip over the defence, Sammon was crowded out by a combination of Cameron and Lainton, whilst the Bury goalkeeper pushed away Woolford's half-volley.
Collins head over Woolford's corner, whilst Freeman cut back for Sharp to fire over before boss Adkins made a double change, introducing Wallace and Flynn.
Before they could make an impression, Bury grasped the initiative. From a hopeful ball into the box, Mayor's effort was blocked by Edgar and the ball dropped invitingly for POPE to slot home from six yards.
United had an immediate chance to level but from Flynn's corner, the ball came off Collins' shoulder, whilst Bury's slowing tactics continued, although the visitors came close to a second when Howard had to kick away from Leon Clarke.
The Blades, however, were soon level, and it was one of the substitutes that was instrumental. The turn from Wallace beat both Riley and Brown and a combination of both hauled him down. It was right on the edge of the penalty area but referee Webb pointed to the spot and SHARP took responsibility to drilled home in front of the Kop.
From another Flynn corner, Collins was involved once again but Lainton saved with his chest. In an offensive move, Adkins threw on McNulty for Woolford but the Blades were undone with the next attack. Brown laid off to RILEY, who smashed an unstoppable 35-yard effort across Howard and into the top corner on 83 minutes.
A melee on 84 minutes helped Bury slow down the action, Leon Clarke and Sharp getting booked to take the yellow card count to eight, which later became nine.
Late on United's passing became longer but the chances dried up, whilst five minutes of added time saw Bury hit on the break again. This time Hussey's ball over the top saw Leon CLARKE nudge McEveley away from the ball before chipping over Howard.
Blades: Howard, Freeman, Basham, Sharp, Collins, Woolford (McNulty 81) Sammon, McEveley, Campbell-Ryce (Flynn 60), Reed (K Wallace 60), Edgar.
Unused: Scougall, Alcock, Higdon, Long.
Bury: Lainton, Riley, Hussey, Tutte (Brown 37), P Clarke, Mellis (Pugh 70), L Clarke, Mayor, Jones (Pope 53), Soares, Cameron.
Unused: Dudley, Rose, Ruddy, Foulds.