At the Oval, Matthew Shevlin, a goalscorer in both of Coleraine’s opening two games, should have done better when presented with a great chance inside the opening five minutes.
The in-form striker latched on to a poor back pass from James Singleton but he was forced wide by Glentoran ‘keeper Daniel Gyollai and the chance was gone.
Cammy Palmer tried his luck from distance just minutes later but his 25-yard right foot effort curled just the wrong side of Rory Brown’s far post.
Jamie McGonigle was similarly off target with a long range effort just after the half hour and Shevlin was denied by a smart save by Gyollai as the visitors finished the first half strongly.
The home side started the second half strongly and had strong claims for a penalty as Cammy Palmer’s shot appeared to strike Coleraine defender Cameron Stewart’s hand but referee Jamie Robinson was unmoved.
They came agonisingly close to breaking the deadlock with 15 minutes remaining when sub David Fisher’s free-kick whistled past Brown’s post from fully 30 yards.
The Coleraine goalkeeper had to be alert, too, to reach up and tip over Jordan Jenkins’ goalbound header from a deep Fuad Sule cross to the back post.
And he proved his worth again in added time as he stood tall to deny Fisher from Niall McGinn’s whipped free-kick from out on the touchline.