Substitute Chris Porter struck twice in the dying seconds to down Nottingham Forest and set up a possible Steel City derby in the FA Cup quarter-finals.
Although deep in a relegation scrap in the third tier United have been a different creature in the cup, knocking out Aston Villa and Fulham before adding Forest to the list with a remarkable comeback.
The Blades, comfortably the lowest-ranked team left in the draw, trailed to Jamie Paterson's first-half header until the 68th minute when a goalkeeping howler by Dorus De Vries allowed Conor Coady to tap into an open net.
Then Porter arrived as an 87th-minute substitute and produced some authentic cup magic as he converted a last-minute penalty before prodding home again in injury-time.
The result raises the tantalising prospect of a clash with Sheffield Wednesday - should the Owls see off Charlton in their own rearranged fifth-round clash.
With almost 26,000 packed into Bramall Lane - the highest gate of the season - the match had an intense atmosphere from the off and that soon translated to the players, who contested a scrappy but high-paced opening.
Forest had chances for Darius Henderson, Paterson and Greg Halford in the opening stages, but Harry Maguire and Neill Collins dealt comfortably with Andy Reid's deep balls over the top.
Maguire found himself on the end of a penalty appeal when Simon Cox tumbled in the six-yard box but the linesman had a perfect view and saw nothing untoward.
The Blades might have had their reward in the 25th minute when Forest committed too many bodies forward and invited a counter-attack.
Jose Baxter collected the ball inside his own half and charged on unchallenged to the edge of the area. He had Stefan Scougall peeling away to the right but instead opted to shoot and left De Vries with an easy save.
It took Forest just three minutes to punish that missed chance.
Reid turned a decent spell of possession into something more, advancing down the right before delivering a pinpoint cross. Paterson, edging out his marker, nodded home.
United had one more chance to get on the scoresheet before the break, Baxter this time choosing the right pass when he reached the box.
Scougall managed a decent connection as he aimed for the bottom corner but De Vries was equal to it.
By half-time the quarter-final draw had been made and United came out like a team intent on setting up a derby date.
Forest were pushed back early in the second period, Gonzalo Jara blocking bravely as Maguire smashed a loose ball goalwards following Baxter's corner.
Scougall went closer, firing through a crowded area from 20 yards only for De Vries to make another calm save.
The visitors, subdued since the interval, clicked into gear as the hour-mark approached, Paterson producing a curling effort that left Mark Howard at full stretch.
United were unperturbed and raced forward once more.
Forest survived a penalty appeal when the ball appeared to strike Fox on the hand but the leveller arrived just a minute later.
De Vries was entirely culpable, somehow losing control of John Brayford's speculative cross and tangling with defender Jamaal Lascelles as Coady swooped to poke into an open net.
Reid almost restored the lead within two minutes but Howard pawed the Irishman's free-kick over the bar.
But United were in no mood to lie down.
With a minute of normal time left Murphy's cross was handled by Lascelles and Porter, despite being on the pitch a matter of seconds, did not hesitate with the spot-kick.
The crowd went wild but there was more yet to celebrate as a rattled Forest defence allowed Porter to steal into the six-yard box and bundle home a second.