With manager Daniel Farke in the stands serving a one-match ban for being booked for the third time this season amid the celebrations of his side's winner against the Black Cats last week and skipper Ethan Ampadu out with a knee injury, the away side made a very uncertain start.
Meslier nearly turned the ball into his own goal from a Sydie Peck corner and was caught under a long throw in the opening 10 minutes.
The Frenchman then made a super save from O'Hare's deft header after Ben Brereton Diaz's cross, but his luck quickly turned as he knocked the loose ball into the corner of his net after Campbell headed the rebound against the post.
Leeds twice got in behind the home defence in the closing minutes of the first half, but both times Manor Solomon was unable to take advantage.
Meslier made a good stop to keep Campbell out at the start of the second half and left-back Firpo then missed a good chance when he miscued a header from Tanaka's cross.
The Dominican made no such mistake a few minutes later, powering home an excellent header from James' cross to spark pandemonium in the away end.
Vini Souza drew a save from Meslier as the Blades looked to retake their lead in both the game and the title race, before substitute Willy Gnonto forced a smart save from Cooper from 18 yards.
The reprieve was brief for the home side.
Tanaka headed in at the back post from the subsequent corner and in the blink of an eye it was 3-1, Leeds top scorer Piroe collecting James' pass from the right before hammering a beauty into the top corner from 20 yards.
Both managers spoke before and after the game about how this match would not be defining in the promotion race, but it is hard to see past Farke's side taking the title now after two victories in which they showed the mentality and quality of champions.
Leeds, who have not lost in the Championship since 30 November, welcome play-off-chasing West Bromwich Albion on Saturday (12:30 GMT), while Sheffield United must pick themselves up for a trip to Queens Park Rangers (15:00) on the same day.