United had the better of the first half and Os defender Tamika Mkandawire cleared off the line moments before Jermaine Beckford had the ball in the net only to be ruled offside.
Leeds went ahead on 16 minutes when Bradley Johnson put the final touch to a Neil Kilkenny free-kick.
Orient keeper Glenn Morris made crucial saves from Jonathan Howson and Dougie Freedman before Beckford escaped onto a quickly taken free-kick but shot wide.
But he made no mistake on 50 minutes when Dougie Freedman escaped on the left and laid a chance in his path for his 20th league goal of the season.
Beckford was later forced off with a leg injury while Paul Huntington played with a head wound bandaged as Leeds saw the game out.