The Blades made it six unbeaten on the road in npower League One thanks to a solid display on a cold night at Gigg Lane.
Two of Danny Wilson's January captures claimed the goals to beat Kevin Blackwell's Bury.
Jonathan Forte scored his first Blades goal for more than eight years to give United a half-time lead and then Jamie Murphy's first for the club made it two on the hour.
Boss Danny Wilson named an unchanged squad for the visit to Gigg Lane to take on Kevin Blackwell's Bury, keeping faith with the same starting XI and substitutes from the victory at Shrewsbury at the weekend.
In a low-key opening ten minutes, Murphy fired over after Maguire stepped out of defence with the ball, whilst a cross from Flynn was turned back towards his own goalkeeper by Zubar, whilst for Bury, Schumacher blasted a free-kick well wide.
Ajose fired wide on 15 minutes after he was presented a chance from a Blades error but the Bury man went closer soon after, a speculative shot on the turn from the edge of the box forcing Long to concede the game's first corner with a diving save.
United's first corner, on 21 minutes, caused Bury problems. From Flynn's delivery, Collins almost connected before the ball hit a knee in a crowded penalty area and forced goalkeeper Carson into evasive action, saving at his near post.
Around the half-hour mark, as Forte battled for possession with Zubar, Flynn stole in to nick the ball but the subsequent shot, with his unfavoured left-foot, was straight at Carson, whilst at the other end, Long was called into action to deal with a number of testing backpasses from his defenders. Also for the home side, Thompson had a shot blocked by McMahon and Zubar fired considerably wide, before the Blades grabbed the lead.
With 38 minutes gone, Kitson took down Long's kick and laid off to Doyle, whose pass enabled FORTE to turn inside Eastham before slotting past Carson with a right footed effort from a central position.
For the remainder of the half the Blades comfortably protected the slender advantage and could have extended the lead but Flynn fired wide from another Kitson knockdown in the solitary minute of added time.
Bury went close to levelling with the first chance of the second period but central defenders Eastham and Zubar challenged each other to connect with Schumacher's inswinging free-kick, the ball flying over the crossbar as a result - the home side were then made to pay on the hour.
A Blades corner was half-cleared but Doyle found MURPHY in space and he beat his marker, found more room and opened up his body to curl into the far corner from the left. The Scot almost added his second in a Blades shirt soon after, firing wide from 25-yards, which was quickly followed by Forte shooting into the sidenetting.
Robson was the first United substitution introduced, taking the place of Forte with little over 15 minutes to go, and with the thousand plus Blades fans making plenty of noise, the visitors were happy to slow down the game and keep the ball as far away from Long's goal as possible, although Healy struck a post from an offside position on 84 minutes.
The closing minutes were incidental, apart from Ironside replacing Kitson, but Unitedites were not fussed as they began their trip back across the Pennines with three more points safely in the bag.
Bury: Carson, Skarz, Eastham, Schumacher (Worrall 63), Bishop (Healy 82), Ajose, Regan, Zubar, Thompson, Ebanks-Landell, Soares.
Unused: Jones, Carrington, Belford, Carole.
Blades: Long, Higginbotham, Maguire, Flynn, Doyle, McDonald, Kitson (Ironside 90), Collins, Forte (Robson 74), Murphy, McMahon.
Unused: Westlake, Hill, McFadzean, Coyne, De Girolamo.