The hosts dominated the first half and deservedly took the lead in the 37th minute when Wes Thomas fired home from the left side of the visitors’ box after collecting a pass from Brek Shea.
Shea could have doubled City’s advantage in the opening minutes of the second period had his header from close range been on target.
Clayton Donaldson came close for the home team soon after, before Alex Mowatt had a shot from outside the box saved.
Billy Sharp had a chance just before the hour mark, as Leeds started to increase pressure and hit back for the equaliser.
The West Yorkshire team eventually got their reward in the 76th minute when Mowatt found the target from inside the City penalty area with his left foot.
Leeds could have even won the match in injury time had Rodolph Austin’s attempt not been saved.