Colin Nixon's late dismissal completed a miserable Setanta Cup quarter-final first leg for the Glens in Sligo.
Rovers dominated the game and went close before Romauld Boco's deflected header from a free-kick put the hosts ahead on 37 minutes.
Glentoran improved after the break and keeper Richard Brush made a superb save to keep out Ciaran Martyn's effort.
Mark Quigley finished a good move to make it 2-0 before Nixon was sent-off for two yellow cards after 83 minutes.
Ross Gaynor headed just wide for Sligo two minutes before Boco scored a deserved opener.
Glentoran had to wait until the 51st minute for their first chance, with Darren Boyce shooting wide from a Richard Gibson cross.
Rovers almost scored a third in the dying minutes with Gaynor, Lee Lynch and Boco going close.