It was Charlton who took control of the early stages, and Kevin Lisbie tested Ben Hamer with seven minutes on the clock.
Orient passed up a glorious chance to take the lead moments into the second period when David Mooney stood over the penalty spot, but he fired his spot kick wide.
Charlton continued to push as the second half advanced, and Danny Green struck the post with a fine effort after 75 minutes.
The two sides could not be separated in normal time, and Green so nearly added a second moments into extra time but his effort just missed the post.
Leon Cort was next to come close for Charlton as the Championship club dominated the extra time period, but the match headed for penalties - which Orient won 4-3.