The Leeds midfielder converted second-half substitute Robert Snodgrass' cross in the 84th minute to settle a disappointing encounter that ignited in the final 10 minutes in front of 33,622.
Snodgrass, in only his second appearance this season, was sent off in the 89th minute for his second yellow card and Leeds were then saved by the woodwork in time added on.
Nick Montgomery's curling cross was met by Jon Ertl and, with Leeds goalkeeper Shane Higgs beaten, the ball came back off the crossbar.
There was still time for Blades substitute Jamie Ward to be shown a straight red card for a reckless late challenge on Neil Kilkenny.
Rival managers Simon Grayson and Gary Speed, who signed for Leeds as apprentices on the same day in 1984, have enjoyed similar results this season.
And there was little to separate their sides until a moment of inspiration from Snodgrass helped secure Leeds their first victory over the Blades since 1993.
George McCartney made his debut for Leeds at left-back and Lloyd Sam and Luciano Becchio both returned.
Nyron Nosworthy, in for injured Blades captain Chris Morgan, and Stephen Quinn were Sheffield United's two changes.
Ched Evans thundered an early free-kick into the Leeds wall on the edge of the penalty area in the third minute, but it was the home side who dominated the first 25 minutes without creating any clearcut chances.
Then a sweeping Leeds move ended with Bradley Johnson hurling himself onto Max Gradel's cross and directing a superb header towards the top corner, only for Blades goalkeeper Steve Simonsen to push the ball away at full stretch.
McCartney was booked for an ill-judged challenge just before the break and then curled a right-footed shot over the crossbar after cutting inside, but neither goalkeeper was troubled again before the half-time whistle.
Former Leeds skipper Lucas Radebe received the biggest cheer thus far when introduced to the crowd during the interval, the South African relishing a return to the city to promote his book.
But the 'Chief's' presence hardly inspired Simon Grayson's side, who were lucky to go unpunished when caught dithering at the back three minutes after the restart.
Passes from both sides went astray and play was too often disrupted by niggling fouls that referee Anthony Taylor was keen to penalise.
Blades manager Speed sent on Jamie Ward for Stephen Quinn in the 59th minute and Leeds favourite Robert Snodgrass replaced Lloyd Sam 60 seconds later.
But the pattern remained much the same and Grayson swapped Gradel for Neil Kilkenny in the 72nd minute and Davide Somma for Ross McCormack soon after in a bid to unlock a well-organised Blades defence.
But Snodgrass wriggled free inside the area and cut the ball back for Johnson to convert from close range with six minutes left.
Leeds looked to have snatched it, but after Snodgrass was dismissed for a second yellow card, Ertl's header hit the crossbar and Ward was shown a straight red card for a clumsy tackle on Kilkenny.