The Blades looked dead and buried with almost an hour of a pulsating second leg of the semi-final at Bramall Lane gone as they trailed to Nottingham Forest goals from the prolific David Johnson and Andy Reid.
But as so often this season, the Blades simply do not know the meaning of defeat as they proceeded to dig deep into their reserves of team spirit to book a May 26 date at Cardiff's Millennium Stadium with Wolves.
Manager Neil Warnock is still on course for a nap hand of play-off successes after twice guiding Notts County to promotion via the backdoor, along with Huddersfield and Plymouth.
Every one of Warnock's players can consider themselves heroes on a night to remember, none more so than Michael Brown who initially launched the comeback, then Steve Kabba for the equaliser to force an extra 30 minutes.
Paul Peschisolido then scored a stunning individual goal to give United the lead with just eight minutes of extra time remaining, prior to Forest skipper Des Walker heading home the Blades' fourth.
United skipper Rob Page's own goal set up a tense finish as it put Forest back within striking distance, but United eventually held on before receiving a standing ovation from their own supporters.
Forest had taken the lead on the half hour courtesy of an inexplicable mistake from the usually reliable John Curtis, who has been an impressive acquisition for Warnock.
The on-loan full-back from Blackburn, despite being 30 yards from goal and facing Paddy Kenny, chose to play the ball sideways instead of a pass back.
Johnson needed no second invitation to run on and smash the ball past Kenny, with Curtis' reaction - bent over and with hands on knees as he looked to the ground below to open up and swallow him - telling the story.
Johnson foolishly celebrated in front of The Kop, with the reaction from a number of Blades fans one which was totally expected, although mercifully none ran onto the pitch to confront him.
Prior to that, and given the occasion and what was at stake, United played arguably their worst 45 minutes of football at Bramall Lane this season.
In front of a sell-out crowd, nerves seemed to take hold, which was surprising in light of the fact Warnock's side had beaten Premiership Leeds (twice), Liverpool and Sunderland in the FA and Worthington Cups this season.
Those ties were just four of the 10 United had won in front of their own fans during what has been a remarkable campaign, one which led to Warnock finishing runner up to Everton's David Moyes in the League Manager's Association Manager-of-the-Year awards on Monday.
But Warnock watched his side strangely struggle as Forest comfortably coped with a subdued Blades frontline in the opening 45 minutes which produced just two meaningful chances for the home side, with both falling to Dean Windass.
The first was not until the 10th minute when a short corner between Brown and Michael Tonge led to the latter cutting inside Reid and delivering a low, curled ball into the six-yard box.
Diving Forest goalkeeper Darren Ward tipped the ball on to the far post, with the deflection enough to prevent the arriving Windass from steering home the opening goal as his eventual touch was wide.
Windass was then guilty of missing United's best opportunity of the first half 10 minutes later after a Rob Kozluk throw had been knocked on in the heart of the area by Page.
An all-alone Windass at the far post was given a free header, but with the goal gaping, his downward header was straight into the arms of a grateful Ward.
After Carl Asaba had narrowly volleyed wide in the 35th minute, Forest could have left the Blades with a second-half mountain to climb as Reid picked out Marlon Harewood with a fine pass, but his angled drive shaved the right-hand post.
When Republic of Ireland international Reid then drove home Forest's second in the 58th minute, after fine approach play involving Riccardo Scimeca, Darren Huckerby and Matthieu Louis-Jean, United's cause seemed a lost one.
But you write off Warnock's side at your peril and so it proved for United were on level terms just 10 minutes later, however, somewhat fortuitously with their opener on the hour mark.
But when you are almost down and out, you need a stroke of good fortune if you are to have any hope of staging a salvage operation.
It came in the form of a wicked deflection from a free-kick as Brown's 22nd goal of the season struck Walker, standing on the edge of the wall, totally wrong-footing the helpless Ward.
The momentum was now with United and eight minutes later Kabba, on at the start of the second half for Windass, thundered a stunning volley past Ward for his 11th of the season following a long punt upfield from Kenny.
United then poured forward in search of the winner, but it never materialised, so resulting in 30 minutes of extra time, but with no golden goal or away goals rule.
Peschisolido, on the field just seven minutes as a half-time in extra time sub for Peter Ndlovu then jinked his way past Louis-Jean and Walker before delivering the coup de grace in the 112th minute, again after Kenny had lumped the ball upfield.
Walker then made it 4-2 minutes later as he headed past Ward, reminiscent of his goal in the 1991 FA Cup final when he again scored an own goal in extra time to hand Spurs the trophy.
Hjelde's close-range strike, after Kenny had fumbled a Huckerby drive, only added to the drama of what was one of the most memorable matches since the inception of the play-offs.