Robert Snodgrass put United ahead with a superb solo effort with 17 minutes gone before Max Gradel doubled their lead with a clinical finish five minutes into the second half.
The home side pressed for a way back into the game and hit the bar twice in a matter of seconds but it was not to be their day and Leeds held on for the win.
Bristol City made a bright start and fashioned the first meaningful chance of the game when Jamie McAllister got forward and crossed for Martyn Woolford who headed over.
However Leeds went in front after 17 minutes through a fine goal from Snodgrass.
The Scot collected a pass from Gradel and turned superbly before fashioning some space and slipping the ball past Bristol City goalkeeper David James.
Leeds immediately went in search of a second and the impressive Snodgrass left fly with a shot from 25 yards but James made a fine save to tip the ball round the post.
The home side eventually found their rhythm but Louis Carey fired over from 20 yards.
With half-time approaching Marvin Elliott had a sight of goal but could not direct his shot on target as the Robins finished the half strongly.
Bristol City continued where they left off at the start of the second half with Woolford and Brett Pitman both firing wide.
With 50 minutes gone Leeds delivered another sucker punch when Snodgrass' shot was deflected into the path of Gradel who swivelled and finished well past James.
It almost got worse for the Robins a minute later when Snodgrass found Bradley Johnson with a pinpoint cross and his header just went over.
Bristol City pressed forward in search of a way back into the game and Andrew Keogh had a chance from six yards out but Andy O'Brien made a good block.
At the other end Jonathan Howson played in Gradel but he fired over with James scrambling.
The game was going from end to end and Leeds had goalkeeper Kasper Schmeichel to thank for keeping their two-goal lead intact when he made a good reaction save from David Clarkson's shot.
The Robins were left wondering quite how they did not score with 75 minutes gone when a goalmouth scramble saw Albert Adomah hit the bar before Elliott also hit the bar with the follow-up shot.
Woolford had a shot blocked by Bruce late on but Leeds were not to be denied and saw the game out.