Ciaran Martyn's strike gave the Glens their first league win at Windsor Park for 11 years as they moved level on points with leaders Linfield.
Martyn squandered a good chance before firing in on 22 minutes after keeper Alan Blayney punched out Gary Hamilton's free-kick.
The Blues rarely threatened although it needed a fine Elliott Morris save to keep out Chris Casement's free-kick.
Glens substitute Martin Murray wasted two late chances to seal the win.
Martyn should have put the visitors ahead in the early stages but lifted the ball over the bar from four yards.
Linfield full-back Jim Ervin dragged a shot wide before Martyn netted from 10 yards.
The Blues response was tame although Daryl Fordyce forced Morris into two saves just before the break.
Blayney was the busier keeper at the start of the second half as he denied Gary Hamilton and Murray.
The champions failed to muster any serious threat from open play and only Casement's free-kick gave the Windsor faithful a glimmer of hope.
Murray missed out twice in the dying minutes, first side-footing straight at Blayney and then heading wide from eight yards.
"To come here and show such charcater and mental toughness was very, very pleasing," said Glentoran boss Scott Young.
"We knew it was going to be tough but Elliott did not have to make any outstanding saves and to get a clean sheet is fantastic.
"It's hard to comprehend that we had not won here in the league for over 11 years - I'm very proud of the lads and there is still 40 to 50 per cent more to come from this team."