Yeovil Town have gone into half time ahead courtesy of a James Hayter goal.
The home side came into the Cup match on the back of a poor run of form in the Championship, though Hayter's early header has so far proved the difference.
Hayter scored only his second goal of the season with 12 minutes on the clock, converting a Shane Duffy cross.
Orient have matched Yeovil in terms of possession, but have failed to create any real chances in the opening 45 minutes.