Substitute Paul Peschisolido ensured team-mate Michael Brown's birthday celebrations went with a bang when he snatched a last-ditch winner to finally kill off Ipswich in this FA Cup fourth round tie.
Peschisolido struck from close range to break Town's hearts with an 89th-minute decider after the visitors had fought their way back from 3-0 down inside a remarkable four minutes.
Brown, who was 26 on Saturday, fired the Blades ahead with a well-taken 19th-minute goal and then, after defender Phil Jagielka had added a second on 31 minutes, smashed a brilliant 30-yard volley past Andy Marshall to make it 3-0 with just 26 minutes remaining.
But Joe Royle's men dragged themselves back on to level terms as defender Thomas Gaardsoe, Tommy Miller from the penalty spot and teenage substitute Darren Bent all found the back of the net, only for Peschisolido to dash their hopes.
If the disappointment of Tuesday night's Worthington Cup defeat by Liverpool was having an effect on Neil Warnock's players, it certainly did not show before the break as they made the most of their share of a reasonably even game to fire themselves into what looked like a winning position.
Neither United's Wilko de Vogt, in for the injured Paddy Kenny, nor Andy Marshall had a save worthy of the name to make in the opening 15 minutes or so as their outfield colleagues failed to find the killer pass when it mattered most.
But it was something special from Brown which set the game alight with 19 minutes gone.
The former Manchester City midfielder - sold to the Blades by Royle
during his time at Maine Road - picked up possession some 35 yards out from goal and, after homing in on the target, curled a low right-foot shot past the helpless Marshall from the edge of the box to give his side the lead.
Spaniard Pablo Counago wasted a glorious opportunity to level from Jermaine Wright's inch-perfect 26th-minute cross, and the miss proved costly as United struck once again.
On-loan Striker Tommy Mooney, making his first start for the club, headed a Wayne Quinn corner against the post, and Jagielka was on hand to slam the loose ball home to make it 2-0.
Royle replaced wing-back Fabian Wilnis with teenage midfielder Darren Ambrose at the break then sent on another 18-year-old, Darren Bent, for Magilton on 57 minutes, but it was United who continued to dominate.
And it was the latter who almost got the visitors back on track when his explosive run down the right took him past Blades skipper Robert Page and into the penalty area, but when he laid the ball on a plate for Ambrose, the youngster blasted high over with the goal at his mercy.
Ambrose was just as wasteful a minute later after being set up by Miller, but he was handed a lesson in finishing by the impressive Brown on 64 minutes.
Quinn's long free-kick was cleared to the midfielder 30 yards out, and he unleashed an unstoppable volley which screamed past Marshall and into the back of the net.
But, just as it looked as though the tie was over, Town hit back in astonishing fashion.
Gaardsoe's 65th-minute strike looked little more than a consolation, but after Miller was felled by Jagielka inside the box three minutes later, the midfielder dusted himself down and slotted home the penalty to give the visitors real hope.
And they did not have to wait much longer for the equaliser when Darren Bent exploded down the right once again on 69 minutes, and after muscling his way past Quinn, beat de Vogt from close range.
Ambrose almost atoned for his earlier misses with a long-range shot after de Vogt had strayed from his penalty area to head a deep ball clear, but the keeper recovered well to claw his effort away at the last minute.
But there was to be further drama when, with just a minute remaining, the Town defence failed to deal with Quinn's long throw and Peschisolido fired home from close range to snatch victory at the death.