Coventry had the better of the first half with Danny Philliskirk going closest, but he was denied a debut goal when Orient defender Nathan Clarke cleared off the goalline after the ball had ricocheted the striker's way.
Cyrus Christie also had a good chance for the visitors three minutes before the break, but struck the side netting after good build-up play.
Orient took the lead in first-half stoppage time. Kevin Lisbie burst forward after picking up possession in midfield and when a challenge failed to arrive he squared for Dean Cox to finish from 18 yards.
The hosts continued to create the better chances after the break. David Bell, making his first start of the season, went close on three occasions, while Christie was a constant threat on the right.
The best of Bell's opportunities came on the hour-mark when he chased down a long ball and cut inside, only to fire into the side netting.