Paul Gallagher's last minute goal secured three vital points for the Blades at Hartlepool.
The loan striker's first goal for the club broke the hearts of home fans who had seen Steve Howard cancel out a first half header from Dave Kitson.
Hartlepool were on top for much of the second half but the Blades cared little when Gallagher coolly slotted home.
Chief Wilson named an unchanged starting line-up for the encounter at Victoria Park - pre-match doubt Gallagher obviously recovering in time to make his fifth consecutive appearance since signing temporarily from Leicester City. There was, however, a change on the bench where defender Westlake took the place of striker Miller. Home boss Cooper made three changes after a disappointing result at the weekend, which included relegating former Blades Academy defender, Horwood, to the bench.
Pre-match rain slickened the surface and caused a few problems under foot early on, whilst home left back Holden quickly displayed that he had a huge throw at his disposal. Kitson was prominent for United, his shot on the turn was not too far away on six minutes and he followed it up with a header from Gallagher's corner, which was blocked.
Maguire picked up the game's first booking, on 18 minutes, for a foul on Sweeney, who from the resulting free-kick, missed a great opportunity to open the scoring but he failed to turn the ball towards goal when he found himself free at the back post.
The rain and wind were causing problems for both sides, highlighted by Howard only being able to parry out from Poole on 26 minutes, fortunately McMahon was well placed to tidy up any ensuing danger.
Within a matter of seconds McMahon was then crucially involved further forward as the Blades took the lead. The full-back whipped in a cross from the right, from which KITSON got ahead of his marker and left goalkeeper Flinders with no chance of keeping out a well-directed header.
Hartlepool hit back and three times in the next five minutes their fans will have thought they should have levelled.
Firstly, from Holden's cross, Howard nodded down and Sweeney was unable to get a vital touch when unmarked once again and then Monkhouse found himself in the clear after a McMahon error but the winger got his shot horribly wrong. Maybe the closest of the three chances arrived on 33 minutes, from a corner, which saw Sweeney head against the crossbar and striker Howard looked favourite to tap in before United's goalkeeper of the same name collected the loose ball.
The Blades coped with Hartlepool's attacking intent and the final chance of the half fell to the visitors but McDonald's long-range effort was straight at Flinders.
Hartlepool whipped in a couple of dangerous crosses early in the second period, whilst United's first chance after the break was a Blackman shot from 20 yards, but he pulled his effort wide. Twice, in the space of five minutes, Poole failed to hit the target after moves began on the home side's right as the visitors faced a spell of pressure.
Wilson felt a change was necessary and introduced Cofie for Blackman just after the hour but Hartlepool's attacking intent continued as the half progressed with balls being delivered towards United's box from all areas, whilst Poole tested the handling skills of Howard on 71 minutes.
There was a little respite when McMahon linked up with Flynn but the former's shot was straight at Flinders, whilst the home side's persistence paid off on 78 minutes. Franks picked up a loose ball on the right and his deep cross was met by HOWARD, who sneaked back onto the pitch after his earlier endeavours, to intelligently head into the top corner.
Gallagher, Doyle and McMahon were booked as frustrations began to show and Wilson introduced Cresswell for Kitson's tiring legs. From Flynn's cross Cofie could not find any conviction on his shot, whilst Cresswell was hurried out of a shot from a corner, following a clever pass from Collins.
With two minutes to go the Blades went close to nicking it when Cresswell could not connect with an inviting cross from Hill but just a minute later the winner did materalise. A ball was played out to the right and from Flynn's cross, in front of the defence, GALLAGHER held his run and sidefooted across the goal and into the corner of the net, in front of the ecstatic Unitedites.
The Blades then held on to possession well in the injury-time period before the Blades fans could continue their celebrations.
Hartlepool: Flinders, Austin, Baldwin, Hartley, Holden, Franks, Murray, Sweeney, Monkhouse, Poole (James 73), S. Howard.
Unused: Humphreys, S. Collins, Horwood, Richards, Lynch, McHugh.
Blades: M. Howard, Maguire, Hill, Flynn, Doyle, Blackman (Cofie 62), McDonald, Kitson (Cresswell 81), N. Collins, Gallagher, McMahon.
Unused: Westlake, Porter, McAllister, Long, Williams.