The home side racked up 27 points courtesy of tries from Ireland internationals Tommy Bowe, Kevin Maggs, Tyrone Howe and Simon Best as they cruised to the win after heading into the break at 3-3.
Two penalties were the lowlights of a scrappy opening period.
Glasgow, hoping to end a run of nine consecutive away defeats, took the lead through the boot of Calvin Howarth but that was cancelled out soon after by Adam Larkin.
Both men missed opportunities to to double their tally before the end of the half.Larkin was back on target soon after the break and prop Simon Best barged over for the first try of the game which Larkin converted to give Ulster a 13-3 lead.
The scoring continued with Bowe producing a 50-metre run for a five pointer.
As Glasgow wilted Maggs got his name on the scoresheer after a quickly taken penalty, and a try from Howe and a conversion from replacement Paddy Wallace rounded off the scoring.
Final score: Ulster 30 (4 tries, 2 conv, 2 pen), Glasgow 3 (pen)