The O's then had to play out an added six minutes of time although they might have doubled their lead when Lee Cook struck the crossbar from 20 yards.
Anthony Griffith had been sent off after 76 minutes for receiving his second yellow card in the space of four minutes, the first for a foul followed by another for kicking the ball away.
But the Londoners battled away in an entertaining game and were rewarded when Mooney popped up to net his 10th goal of the season.
The better of the two sides in the second half, Orient notched the decisive goal when full-back Scott Cuthbert crossed from the right and Mooney stole in unmarked to glance the ball past keeper Marek Stech and into the corner of the net.
Yeovil's best chances came in the opening period but were foiled by O's shotstopper Jamie Jones, who was at full-stretch to turn a shot from Dominic Blizzard around the post before he was extended to collect a header from Jamie McAllister.
Orient then stepped up the tempo in the second period with Moses Odubajo twice going close before Mooney struck.