12 Dec, 14:42
Prop Cian Healy is expected to miss the start of the 2014 RBS 6 Nations after undergoing surgery on his injured ankle on Wednesday.
The wet weather conditions had the biggest say in an attritional first half, at the end of which the Ulstermen held a 6-3 advantage thanks to two Paddy Jackson penalties.
The real breakthrough came in the 61st minute when Chris Henry claimed the victors' only try after a muscular drive from the Ulster pack.
The Warriors hit back with a late touchdown from Fijian replacement Niko Matawalu, but the damage had already been done at that stage.
As the rain poured down from the kick-off, Jared Payne opened in impressive fashion with two terrific high takes. The second of which led to a 51-metre penalty effort that Jackson just missed to the left.
There was plenty of early huff and puff from both sides, Glasgow finding their rhythm in the scrum and the visitors peppering the right touchline with kicks.
Ulster opted for the posts again on the quarter hour mark. The returning Ruan Pienaar had the accuracy but not the required distance from a mammoth 62 metres out.
Centre Peter Horne missed Glasgow's first penalty shot after another strong scrum from the hosts, but he made no mistake moments later as the Warriors took a 21st minute lead.
Within minutes Iain Henderson did well to haul down Heineken Cup debutant Byron McGuigan in the Glasgow 22, creating a simple penalty for Jackson who nailed it for 3-3.
Glasgow captain Al Kellock then came in at the side of a ruck after a good period of Ulster carrying and Jackson mopped up to put the province ahead.
Horne miscued a penalty late on as the Scots enjoyed better territory, although Ulster's tackling was of the first rate variety with Henry, Dan Tuohy and Rory Best particularly prominent.
Andrew Trimble chased down a Pienaar box kick and had the recycle been quicker, an overlap was looming. But an unfortunate knock on from the otherwise errorless John Afoa spoilt the promising attack.
As the rain abated for the second period, Horne failed to reward the home scrum as he suffered his third penalty miss of the night.
Ulster gained momentum as Nick Williams initiated a powerful series of carries from the forwards, with the visiting fans also raising the decibel level.
Glasgow survived having defended stoutly, but Ulster were growing in confidence as Williams and company continued to pick and drive and find holes.
Pienaar dropped a penalty short of the target after good foraging at a ruck from man-of-the-match Best, who was accurate in the lineout and typically busy in the loose.
The key moment came from the restart as Ulster surged forward again, a powerful maul ending with flanker Henry twisting free to ground the ball.
Jackson converted and fired over a subsequent penalty, putting 13 points between the sides with just 15 minutes remaining. Glasgow's error count was increasing, however their scrum was keeping them in the game.
Jackson provided some further cushion with another three-pointer, pushing his own tally to 14 points, before Glasgow picked off a late consolation try.
Ryan Wilson's break down the left, with two minutes left, got the Scots into scoring range and a hanging cross-field kick from Scott Wight was dotted down by Matawalu in the right corner.
Castres Olympique beat Northampton Saints 21-16 in the night's Pool 4 fixture. With a late losing bonus pojnt, the English club are second in the table ahead of their back-to-back clashes with Ulster in December.
|Glasgow Warriors Score Card|
|Ulster Rugby Score Card|