A Rickard Palmberg hat-trick and an impressive display in net from Stephen Murphy with 27 saves helped the Giants to the Friday home win.
The Giants now sit in third place with 34 points from 27 games, four points behind the Sheffield Steelers in first place with 38 points from 29 games.
The Giants opened the scoring in Friday’s Elite League clash when Rickard Palmberg rounded Patrick Killeen in the Glasgow goal and cooly slotted home at 16:47, assisted by Jordan Smotherman.
Belfast doubled their lead at 28:22 when Elgin Pearce was on hand to finish off the move he started, assisted by Rickard Palmberg and Curtis Hamilton.
Little over two minutes later and it was 3-0. Palmberg was involved again when he snapped home a wrister at 30:39 on the powerplay and assisted by Ryan Lowney and Curtis Hamilton.
Brian Ward added a fourth for the hosts at 36:54 after nice work by Liam Reddox who took a shot on net and Ward cleverly redirected the puck home.
The Giants extended their advantage once again early in the final period when Rickard Palmberg completed his hatrick with a fine solo goal at 41:47, assisted by Liam Morgan.
Glasgow got on the board at 54:50 when Mathieu Roy finished well past Murphy, assisted by Matt Haywood and Travis Ehrhardt.