Despite Oli McBurnie’s second-half opener, his fifth goal in six games, United couldn’t hang on and were pegged back when Troy Deeney equalised for the visitors soon after.
United had chances to win, substitute Billy Sharp seeing his one-on-one shot well saved by John Ruddy, and Norwich's win away at Blackpool saw them move to within a point of Paul Heckingbottom's men at the top of the Championship table.
Here’s how we rated the Blades against the Blues...
5. John Egan 6
Had to be alert at the start of the second half as Birmingham looked to catch United out but their key centre-half snuffed it out. Marshalled the defence well against a difficult opponent in Deeney Photo: George Wood
6. Rhys Norrington-Davies 6
Came up with a superb block to prevent Chong making it 1-0 early on when the Birmingham man found some space in the United box and struck his shot well. Good cross in the second half picked out Ndiaye but his header went wide Photo: Ashley Crowden
7. Reda Khadra 5
Lined up on the left wing and had a nervy start when he miscontrolled a pass out for a throw in but his wicked cross almost produced an early goal, going just wide of Ruddy's goal. Wasn't afraid to try things but a lot didn't quite come off for him before he was replaced just after the hour mark by Bogle Photo: Lexy Illsley
8. Ollie Norwood 6
Had a big hand in McBurnie's goal which came from his free-kick and some of his passing in the first half, especially first-time passes to keep United's momentum going, were exceptional. Booked in the second half for fouling Chong, who went down about five seconds later, Photo: George Wood