Shane Jennings scored his first goal of the season on eight minutes to secure victory for Coleraine, who remain in fourth place in the Premiership table.
Jennings knocked in the rebound after his initial effort had hit the post.
Curtis Allen missed a number of chances to extend the lead, while Ruairi Harkin and Stephen Lowry also went close.
For the Glens, Mark Clarke was off-target, David Howland fired straight at Michael Doherty and Andy Waterworth hit the bar and blasted over.
Elliott Morris denied Harkin and twice saved well from Allen.
The Bannsiders will be relieved to pick up three points after having won just one of their previous seven league outings.
The Glens stay fifth in the standings.