Another moment of magic from sub James McAtee, off the bench at half-time, was the difference between the two sides, while Iliman Ndiaye had a later strike ruled out for a foul on goalkeeper Max O’Leary by Billy Sharp.
Here’s how we rated United's players after what could prove to be a huge win in the context of their promotion push...
1. McAtee the matchwinner
James McAtee of Sheffield United appeals for a foul against Bristol City: Simon Bellis / Sportimage Photo: Simon Bellis
2. Adam Davies 6
A spectator for much of the game, despite City posing a threat going forward, but had to be alert to race off his line and clear with Sykes bearing down on him and looking to put his side ahead. Well protected by the defence in front of him Photo: Andrew Yates
3. George Baldock 6
Had a rare difficult time of it defensively as Bell down the City left caused him problems in the first half and may have had his heart in his mouth when he tangled with the City man as he looked to race clear on goal, only for the ref to wave away the visitors' appeals. Improved after the break when he had more chance to steam forward with the ball and look to make something happen Photo: Simon Bellis
4. Anel Ahmedhodzic 7
Back in the side after missing out against Cardiff, the Bosnian was forced to make a superb early recovery challenge to snuff out the danger from Sam Bell as he looked to test Davies from a tight angle. Gave United fans something of an injury scare when he stayed down in the second half holding his shoulder after colliding with O'Leary but he soldiered on. Even tried this acrobatic overhead kick but couldn't make contact Photo: Andrew Yates