The Blades were pegged back in a first half that they dominated, but they showed good resilience to come away with all three points thanks to a late David Brooks goal.
Less than 10 minutes after being brought off the bench, the 20-year-old tucked the ball past Andy Lonergan to earn the Blades a fifth win in six outings - enough to send them above Cardiff City and Wolverhampton Wanderers into first place.
The visitors were ahead with just over two minutes of the contest played through Billy Sharp, who peeled away at the back post to head Mark Duffy's cross over the line - his fifth goal in four starts against his former side.
Duffy was the star man in the opening 45 minutes, floating in another delightful cross for Leon Clarke to turn narrowly wide, before George Baldock shot right down the middle after being teed up by his midfield teammate.
Sheff United had another big chance to double their advantage with 27 minutes of the match played, only for Lonergan to produce a big save to deny Sharp at the front post following an error from Matthew Pennington.
Despite failing to register a single shot of any sort up until that point, or even so much as have a touch in the opposition box, Leeds were level soon after thanks to a Kalvin Phillips drive.
The Blades will wonder just how the scores were level at the midway stage, though, adding another miss to their collection after Lonergan kept out a completely unmarked Sharp from close range two minutes before the break.
Leeds nearly edged in front from the first meaningful attack of the second half, with Samuel Saiz putting his foot through the ball and picking out the post.
The Whites could consider themselves fortunate to see the remainder of the game through with 11 men, however, as goalscorer Phillips lunged in on Baldock and somehow got away with just a yellow card.
Clarke tested Lonergan from the tightest of angles as the two sides traded blows in a feisty Yorkshire derby affair, which sparked back into life with 10 minutes remaining.
The introduction of Brooks proved pivotal, as he set up Clarke for a decent attempt before then going it alone, slotting the ball across Lonergan once picked out by Duffy to earn bragging rights and all three points.