Hull City netted a fortuitous second half goal and the Blades had a last minute header ruled out for offside at Bramall Lane on Monday evening.
Hull created the first chance, Edwards shooting at Ramsdale; but the best opportunities of the first half fell to the Blades. Hallam had a shot saved and Chapman and Scougall had efforts blocked.
A header from defender Cummings was on target but Batty cleared off the line and then the best chance of the half also fell to United on 40 minutes.
Annan wasted possession in his own half, allowing Brooks and Hussey to link up on the left and Chapman's shot was heading for the top corner before a brilliant fingertip save from goalkeeper Mannion.
The early stages of the second half failed produced many chances, although United looked the more likely to score. Kelly, on as a substitute, and Brooks both went close. At the other end, Cummings provided a timely clearance to cut out Hinchliffe's cross.
However, Hull grabbed the lead midway through the half, fortuitously. ANNAN found space on the right and a heavy first touch encouraged Ramsdale off his line but the goalkeeper's clearance cannoned off the Hull man and spun into the net from 18 yards.
Chapman attempted to restore parity with a first time shot but Mannion saved and on 75 minutes the Blades were indebted to Ramsdale, who, at full stretch, pushed an Edwards header onto a post.
Hull managed the final 15 minutes well, limiting United's forward forages and a last minute penalty claim, when substitute Smith fell, was ignored.
There was a final moment of drama with the penultimate touch of the game. Substitute Burton headed home a Brown cross but was flagged off side.
Blades: Ramsdale, Brown, Hussey (Kelly 50), Whiteman, Cummings, Semple, Brooks, Scougall, Hallam (K. Smith 64), Reed (Burton 83), Chapman.
Unused: Perryman, Gordon.
The full match video is now available on BladesPlayer.TV
First Half Second Half