The home side almost took the lead early on when Sam Byram's volley flew inches past the post, as Leeds made a fast start in the opening stages.
The Lions grew in confidence and almost took the lead a couple of minutes later, as Jos Hooiveld's header from a corner flashed just over the bar.
Leeds got the breakthrough shortly before half time, as Mowatt's free kick took a deflection and gave David Forde no chance in the Millwall goal.
That breathed confidence into Leeds, who almost doubled their lead shortly after as Rudolph Austin's acrobatic effort was blocked by Forde on the goal line.
The home side almost confirmed victory in the 75th minute, as Mirco Antenucci set up Byram at the back post but he blazed the ball over the bar, before Steve Morison later headed over from close range.