Once again, this time against fellow automatic promotion contenders and arch-rivals Leeds, Chris Wilder's men produced all three as a performance of supreme guts and, when it matter most, guile.
The result, which lifted them above Marcelo Bielsa's men in the Championship table, means United enter the international break ranked second. There is, as Wilder warned before kick-off, still plenty of football left to play.
But there is also a growing sense, with this victory coming after a similarly hard-fought win over Brentford in midweek, that something special is happening at Bramall Lane.
Leeds, who finished the contest with Pontus Jansson between the posts following Kiko Casilla's red card during the closing stages, looked crestfallen at the final whistle. United, meanwhile, celebrated three more crucial points. And, perhaps just as impressively, a seventh straight clean sheet.
Chris Basham's 71st minute goal, his fourth and potentially most important of the season, helped the visitors negotiate safe passage through the game.
From Leeds' perspective, the lunchtime fixture was a lesson in what can happen when you do not take chances.
Dominant for the most part before the interval, they failed to translate that into an advantage and paid the ultimate price when Billy Sharp's assist sent his colleague darting through.
Anticipating the midfield would be a maelstrom, particularly during the early skirmishes, Wilder named Martin Cranie at centre-half and tasked Basham with protecting Oliver Norwood and John Fleck. United's suspicions proved correct as Leeds, and Pablo Hernandez in particular, came roaring out of the blocks during the opening stages.
John Egan, aided and abetted by Cranie, did well to prevent Patrick Bamford's cross from reaching Dean Henderson and, given his proximity to goal, almost certainly the back of the net. Another opportunity went begging for Leeds soon after, Jack Harrison firing over the crossbar from close range, after Jack O'Connell had smothered Tyler Roberts.
Deep in conversation with his assistant Alan Knill and Matt Prestridge, Wilder was clearly troubled by what he was witnessing. Even more so when Bielsa's players surrounded David Coote following George Baldock's challenge on Jansson even though, producing a yellow rather than a red, the referee correctly interpreted the Swede had made a meal of it.
Although Leeds controlled the vast majority of the first-half, Wilder might actually have entered the interval the happier of the two managers. As his team finally got to grips with the nuances of the system they had been asked to employ, John Fleck saw more of the ball and Enda Stevens began to test his opposite number along the flank. Indeed, a delightful piece of improvisation from the Irishman nearly presented David McGoldrick with a clear cut chance. Casilla, however, was alert to the danger and edged off his line to catch the ball after Stevens had checked back and threaded it behind Luke Ayling.
McGoldrick glanced wide from Fleck's corner and Egan saw an effort scrambled clear following a melee in front of the Spaniard during the closing stages of the half.
After Norwood had fired over the crossbar following some good hold up play by Sharp, backing into his marker before laying the ball into the Northern Ireland international's path, Leeds took charge again. But their failure to engineer a breakthrough came back to haunt them when Basham pounced.
Sharp was the provider, keeping his good friend and fellow captain Liam Cooper at bay before releasing a pass which allowed the 30-year-old to gather momentum as he approached Casilla and find the bottom corner of the net.
The former Real Madrid goalkeeper saw red when he brought down Sharp in the first minute of added time and, having used all three of his substitutes, Bielsa was forced to hand Jansson the gloves.
Leeds United: Casilla, Ayling (Dallas 78), Cooper, Bamford, Alioski, Roberts, Jansson, Hernandez, Harrison (Douglas 56), Phillips, Klich (Clarke 78). Not used: Peacock-Farrell, Berardi, Shackleton, Gotts.
Sheffield United: Henderson, Basham (Lundstram 90), Egan, O'Connell, Stevens, Baldock, Norwood, Fleck, Cranie, Sharp, McGoldrick (Dowell 87). Not used: Moore, Hogan, Coutts, Stearman, Duffy.
Referee: David Coote (Nottinghamshire).