The victory, given to Micky Adams’ side by Eric Lichaj’s second-half own goal and a Bjorn Helge Riise strike, will not drag them out of the relegation places, but it does offer further proof that they have what it takes to avoid the drop.
The Blades were the better side throughout against the division’s top scorers, who have now gone two games without a goal and must now be ranked as firm outsiders to make the second automatic promotion spot theirs, especially as they will be a striker light for three games with Billy Paynter seeing red late on.
Having ended a 13-match run without a win in their last home game against Nottingham Forest, Sheffield United were eager to impress from the off and former Leeds midfielder Michael Doyle signalled his aggressive intent with a leading elbow into Robert Snodgrass’ temple inside the first 60 seconds.
Matt Lowton had the Blades’ first chance when he headed straight at Kasper Schmeichel from a corner, before at the other end, Max Gradel wasted a glorious opportunity for Leeds when he ghosted in to nod Lichaj’s centre wide.
Gradel’s miss seemed to give the home side some impetus, and they were hard done to in the 21st minute when referee Mike Jones brought play back for a foul by Andy O’Brien on Stephen Quinn, wasting the advantage they had with Daniel Bogdanovic in possession in the box.
Former Leeds striker Sam Vokes inexplicably header Doyle’s cross towards the corner flag as the Blades began to dominate, and Schmeichel had to produce a stunning one-one-one block to deny Bogdanovic a certain opener after Ched Evans had set him free with a cute back-heel.
Snodgrass briefly threatened for Leeds, dragging wide following a Gradel break, before two more stunning saves from Schmeichel closed out the half.
First he flew to his left to tip a rising half-volley from Quinn to safety, before he punched an Evans drive over the bar after the Wales striker had been allowed to run at the Leeds defence.
Leeds, who were giving Aston Villa loanee Barry Bannan his first competitive start, switched from their favoured five-man midfield at the interval in a bid to establish themselves in the game.
It was Sheffield who had the opening chance of the half, though, with Evans driving over from the edge of the box, before Bannan flashed wide from 35 yards.
Bradley Johnson should have done better when he connected with a Snodgrass free-kick and Leeds were behind not long after.
With 55 minutes gone, Quinn put Nick Montgomery in on Schmeichel’s goal and his cross was turned into his own goal by Lichaj.
The Villa loanee could do little else with home forwards lurking behind him, and it could have been two moments later had former Blade Leigh Bromby not produced a fine covering tackle to deny Vokes.
Bannan threatened the goal from 25 yards as Leeds looked to hit back, but they were unable to do so and effectively lost the game with 16 minutes left.
On-loan Fulham man Riise had been on the pitch for just two minutes when he broke on to a Quinn pass and, from inside Schmeichel’s six-yard box, drilled home hard and low.
Gradel and Bromby tried and failed to ram home from close range after a scuffle, before Paynter saw red with two minutes remaining following an altercation with Shane Lowry, with the Australian defender suggesting he had been stamped on.