It was Orient's fifth clean sheet in six league and cup games and they overall enjoyed a territorial advantage.
Millwall looked the more dangerous during the early stages. Striker Neil Harris lofted a chance from midfielder David Martin over the top and later shot tamely at keeper Glenn Morris.
A fine move provided striker Sam Parkin with Orient's first chance after 21 minutes but he shot tamely, while the home side had penalty claims dismissed when winger JJ Melligan went down and then saw striker Adam Boyd's shot blocked on the line by Millwall captain Paul Robinson.
The second half was contested at a frantic end-to-end pace but with no significant chances created until Orient substitute Dean Morgan's shot was comfortably held by Millwall keeper David Forde.
At a Millwall corner Robinson had a header scrambled away and striker Lewis Grabban made a long run which came to nothing before a second Orient substitute, Ryan Jarvis, also had a shot held by Forde.