Both sides finished with try bonuses as the defences struggled, Glasgow opening the scoring via Lome Fa’atau after Max Evans had collected his own chip.
Dan Parks added five points with the boot as the Scottish side raced into a 10-0 lead, only for Ulster to rein them in with close-range tries from Isaac Boss and Roger Wilson in a frantic opening quarter.
However, Graeme Morrison split the Ulster centres before offloading to Johnnie Beattie for an unconverted try that gave them a 15-12 advantage at the break.
They quickly stretched their lead two minutes after the restart when Evans broke a raft of weak Ulster tackles to make it over and give Parks a straightforward conversion.
All seemed comfortable for Sean Lineen’s side until prop Moray Low was sent to the bin two minutes before the hour for pulling down a driving maul near the Glasgow line. It was to prove costly as by the time he returned his team mates had shipped 12 points to give Ulster the lead once more. Simon Danielli barged over before Tommy Bowe gathered a Boss kick and danced up the touchline and under the posts to give Wallace the conversion and Ulster a 24-22 lead.
Parks’ second penalty edged Glasgow in front again after 66 minutes and with the visitors now back at full strength, Thom Evans burst through from a Beattie pass to score near the posts to make the game safe.
Tries: Boss, Wilson, Danielli, Bowe. Cons: P. Wallace 2.
Tries: Faatau, Beattie, M. Evans, T. Evans. Cons: Parks 3. Pens: Parks 3.
Bartholomeusz; Bowe, Trimble, Dewey, Danielli; P. Wallace, Boss; J. Fitzpatrick, R. Best, Court; Harrison, del Fava; McCullough, N. Best, Wilson.
McCrea for Danielli (75), Campbell for Boss (73), O’Connor for Court (66), Caldwell for del Fava (47), Dawson for McCullough (56).
Stortoni; Faatau, M. Evans, Morrison, T. Evans; Parks, Gregor; Va’a, Hall, Low; Palepoi, Turner; Brown, Barclay, Beattie. Replacements: Barrow for Faatau (65), Milligan for Va’a (53), Newman for Palepoi (53).
T Hayes (WRFU).