Charlie Taylor threatened again for the visitors when he raided forward on goal after cutting in from the left flank and unleashed a powerful strike which went just over the bar.
Wigan's first effort in the game came when Kim Bo-kyung was afforded space and time on the edge of the area to drill a low strike towards goal, but Bamba was alert to the danger and made the block with his body.
In the second half, the Latics almost took the lead when a loose ball from a corner fell into the path of James McClean, who fired an effort towards the bottom corner, but Marco Silvestri made the stop.
The save was to be crucial as Leeds took the lead on their next attack, as Taylor and Sharp combined to set up Mowatt and he scored his eighth goal of the season with a powerful strike into the top corner.
Leeds nearly doubled their advantage when Taylor capitalised on a mistake in the Wigan defence to drive at goal, but his dipping strike from distance went just over the bar.
The home side pushed to get an equaliser and twice came close twice with minutes as McClean powered a shot at goal which smashed into the side-netting and Sheyi Ojo beat his man down the flank and fired the ball across the face of goal, but no teammate was on hand to turn it into the net.
Wigan had one final chance to earn a point when McClean fired a free kick at goal from outside the box, but in-form Silvestri made an impressive save to tip his strike over the bar and secure the win for the Whites.