In-form marksman Ross McCormack fired the hosts into a half-time lead and doubled the advantage 13 minutes from time.
The hosts started the brighter but, despite enjoying a wealth of possession, the Whites failed to carve through the Latics' rearguard in the early stages.
Nevertheless, McDermott's men were rewarded on 15 minutes, as McCormack hit his 13th of the season to edge Leeds ahead, converting from close range after Tom Lees had headed the ball back across the face of goal.
Consequently, Leeds established daylight in the scoreline through McCormack on 77 minutes when his free kick from the left evaded everyone and went in.
It would prove enough as the Yorkshire-based outfit held out for a comfortable victory.