Jon Parkin had a goal controversially ruled offside in the 7th minute. He stuck the ball in the net after the ball fell his way, but it was unclear whether it was a City or a United player who headed it to him.
Kevin Ellison did well to get a shot on target, saved by Neil Sullivan, before Robbie Blake fired over from 6 yards out from Liam Miller's cross.
Stuart Green and Jon Parkin both came close with shots, and although City were unable to find the breakthrough they certainly enjoyed the better of the first half as the sides went in at the break.
Leeds started the second half brightly, before Green wasted a chance for City by putting it well over.
From a corner, Leon Cort had a header saved on the line by Sullivan, while Miller squandered a shot at the other end as Leeds were looking to get back in the game.
When it was looking like it could go either way, City popped up with a goal 14 minutes from time. Green's cross from the right was headed down by Parkin, and Sullivan couldn't get to it as it went in the bottom corner.
Keith Andrews came close to making it 2-0 but his free kick was well saved by Sullivan, before the Tigers captain gave away a free kick at the other end, but David Healy put it wide.
Hulse shot over in 4 minutes of stoppage time, and City held on to record a third successive 1-0 home win.