Orient will travel to Blue Square Bet Premier club Alfreton in the next round after finally breaking the Tigers' resistance - as they held out until the 87th minute before capitulating.
Blue Square Bet North club Gloucester made the brighter start and after a corner from Lewis Hogg in the second minute, Darren Edwards saw an effort hacked off the line by Jimmy Smith.
League One side Orient grew in stature as the half wore on and only some fine goalkeeping from Mike Green kept them out.
He first denied Cox with a smart reaction stop in the 41st minute and Ryan Brunt then saw a miscued header bounce back off the frame of the goal before the goalkeeper saved well from Mooney two minutes before the break.
Orient always looked the most likely winners in the second half as Gloucester began to tire and Green was finally beaten with three minutes to go as Mooney nodded home Cox's cross.
And Cox himself capitalised on a mistake from Matt Coupe straight from the restart to spare Orient's blushes.