Leeds came within inches of taking the lead at the start of the second half when El-Hadji Diouf's free kick was met by Rudolph Austin, whose header came back off the crossbar.
The visitors were ahead for just six minutes, however, as Albert Adomah netted the equaliser for City with a fine diving header.
Leeds regained the lead with less than ten minutes on the clock when Liam Fontaine failed to clear, allowing Diouf in for his second of the game.
Michael Tonge then looked to have put the game beyond doubt with an unstoppable drive from 25 yards to make it 3-1.
City refused to give up, however, pulling one back courtesy of a Byram own goal, but they couldn't find a dramatic late equaliser as Leeds ran out 3-2 winners.