The Addicks broke the deadlock in a high-tempo derby at Brisbane Road when full-back Simon Francis crossed from the right and midfielder Alan McCormack, unmarked beyond the far post, beat Orient keeper Jamie Jones with a precise header.
Orient equalised after the break when Charlton failed to deal with a cross from the right and striker Scott McGleish swept the ball in from beyond the far post.
Two minutes later, Dailly was red-carded by referee James Linington following a clash with Stephen Dawson.
Charlton survived some fierce Orient pressure, and then in rare breakaway on the hour midfielder Scott Wagstaff was put clear by Lee Martin and finished into the corner.
In added time, Wagstaff laid on the chance for substitute Chris Solly to tap in a third.