Leeds bounced back from their midweek five-goal loss at home to Blackpool to pick up their third away win of the season at managerless Leicester.
Adam Clayton struck the only goal in a game of few chances midway through the second half, firing home an unstoppable long-range effort.
The home side rarely tested new loan goalkeeper Alex McCarthy between the Leeds posts.
Simon Grayson's side move just outside the playoff places to seventh, while the Foxes fall to 12th.