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.
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.
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.
Source: PA
Source: PA