Jermaine Beckford scored the only goal of the game in the 19th minute when he shrugged off Wes Brown and slotted home from an acute angle.
The Yorkshire side also rode their luck as Rooney and Michael Owen missed chances late on as the ball pinged about the Leeds penalty area.
Beckford may have been the winning goalscorer but keeper Casper Ankergren was also a hero for a series of saves to keep United at bay.
Under Sir Alex Ferguson, Manchester Utd had never lost in the FA Cup third round or been beaten by a lower division side.
For the Reds, whilst going forward they created chances their makeshift defence never looked comfortable against the attack minded visitor's.
Leeds boss Simon Gray told ITV 1: "The goal gave us an opportunity to go on and win the game, and with a bit of luck we managed to hang on.
"But full credit to the players they were outstanding today just like all season.
"The player's might have tomorrow off then we start for the Wycombe game at the weekend!"