Jack Butland was called into action early on for the home side, turning behind a deflected free kick to keep the score level.
The Whites began creating chances of their own, and with nine minutes on the clock a penalty appeal was waved down by the referee after Matt Smith had gone down in the box under pressure from Shane Lowry.
Unfazed by the decision, Smith found the back of the net for the game's opening goal shortly after, heading home Connor Wickham's long-throw to make it 1-0.
Martyn Woolford came close to levelling the contest when he was picked out by Ed Upson, but his low strike was kept out by Butland.
Leeds added a second minutes before half time courtesy of Ross McCormack, who slotted home past David Forde after the ball had landed kindly to him in the box.