The visitors would rue big misses in the first half as Junior and Jonathan Russell failed to convert, whilst after the break Matthew Shevlin arrowed wide for Coleraine from close range.
The Glens would make a strong start by controlling large spells of possession and they would go very close to opening the scoring on three minutes.
A cross into the box by Russell found Jay Donnelly but the striker's half-volley dropped inches by the far post.
Coleraine would threaten for the first time on 17 minutes as Dean Jarvis and Lee Lynch combined to tee up Josh Carson who steered over.
Three minutes later, the Glens would launch a quick counter-attack as Cammy Palmer picked up possession in midfield and found Jay Donnelly but his low drive was well held by Gareth Deane.
Warren Feeney's men promised to take the game to the Bannsiders and they should have gone ahead on 24 minutes.
A deep cross into the area by Aaron Wightman met Ruaidhri Donnelly at the back post and his flick found Junior in space but he headed wide from close range.
Crosses into the box were proving to be troublesome for the hosts and a delivery into the box by Palmer was met by an unmarked Russell who headed wide.
The hard-working Palmer would help Glentoran create the final chance of the half as he picked up the ball following a Carson mistake.
Palmer was able to find Junior inside the box but his shot was comfortably held by Deane.
The second half would start with both teams being careless in possession but Deane had to be alert to palm away Jay Donnelly's driven effort from inside the box.
Coleraine lacked any rhythm in their play and were struggling to create any clear-cut chances.
They were almost punished on the counter attack as Daire O'Connor's low effort was batted away by Deane.
Oran Kearney's men would finally have a sight of goal with a quarter of an hour remaining.
Jamie Glackin had the vision to find Shevlin inside the box but he was denied by Aaron McCarey.
Coleraine would have their best opportunity of the game on 83 minutes as two substitutes - Jack O'Mahony and David McDaid - linked up to release Shevlin.
The usually-reliable striker blazed wide as he failed to get himself balanced to convert.
A point apiece for both teams as Coleraine miss the chance to leapfrog the Glens in fifth spot.
COLERAINE: Deane, Kane (O'Mahony, 83), D.Jarvis, Kelly, Shevlin, Carson, Farren, Lynch, Glackin, Wallace, Scott (McDaid, 62).
Subs (not used): Gallagher, A.Jarvis, Mitchell, McCrudden, Devine.
GLENTORAN: McCarey, J.Donnelly, R.Donnelly (McCartan, 71), O'Connor, Singleton, Sule, Palmer (Murray, 79), McClean, Russell, Wightman, Junior (Fisher, 86).
Subs (not used): Webber, Murphy, Kelly, McGinn.
Referee: Ben McMaster.