With the prolific Tommy Bowe, Andrew Trimble and Paddy Jackson for once outgunned by their opposite numbers - Sean Maitland, Tommy Seymour and Finn Russell - Ulster's hopes of a RaboDirect PRO12 play-off spot took a dent.
Mark Anscombe's men are still in second place in the table, but their Scottish conquerors are now snapping at their heels in third with just one point fewer and a game in hand.
Also in the mix and vying for a semi-final berth are Munster, leaders Leinster and the Ospreys.
The two provinces are Ulster's next opponents and in the concluding two rounds and Anscombe's side simply must take points from those interprovincial clashes.
The Ulster cause suffered another setback in the course of tonight's match as both Tom Court and replacement Declan Fitzpatrick were added to the ever-expanding injury list.
Court, Sean Doyle and Darren Cave had all returned to first team duty after not starting against Connacht, while Bowe relocated to the right wing and last week's hat-trick hero Trimble lined up on the left.
Warriors, meanwhile, came into the match with great expectations following an impressive 22-5 away victory over Munster.
The Scots were let off the hook as early as four minutes in when Jackson dragged a penalty wide from the 10-metre line.
Russell made no such mistake four minutes later as he dispatched a central penalty from close range, but Ulster - having absorbed a good 10 minutes of Glasgow pressure - carved out a superb breakaway move.
They made ground firstly through Bowe, then Jackson and finally Ricky Andrew, who showed a superb turn of pace to outstrip half-a-dozen opponents.
Andrew was floored before reaching the try-line, but Ulster came away with points thanks to three elementary penalties in quick succession from Jackson.
Ryan Wilson was yellow carded on 25 minutes for handling on the ground while Ulster captain Johann Muller had possession of the ball, and the visitors went on to boss the majority of the second quarter.
Jackson was then unlucky to strike an upright with a further penalty attempt on the half hour.
Glasgow reasserted themselves as half-time approached, with Luke Marshall having to put in a sublime try-saving tackle on Mark Bennett five metres from the whitewash after the centre had ripped through the Ulster defence.
There was still time left in the half, however, for Glasgow to build again, and their efforts were rewarded.
Russell capitalised on a surrendered ball at an Ulster scrum to find Maitland and the winger, cutting through on a nice angle, twisted his way out of tackles from Paul Marshall and Doyle for a converted try.
10-9 down at the break, Ulster leaked three more points when Russell split the posts. It was a double blow as flanker Doyle was sent to the sin-bin for the same offence as Wilson.
Keen to use their numerical advantage up front Russell opted to kick his next two penalties to the left corner. A huge drive from the subsequent lineout saw former Ulster winger Seymour touch down, with the try expertly converted from an acute angle by their in-form out-half.
The Ulster response was spirited, with Bowe looking odds-on to score from Jackson's pass on 57 minutes only for a fully-committed tackle from Seymour to knock the ball from his grasp.
Then a big push from a close-in Ulster lineout on the hour had number 8 Nick Williams lunging for the line.
However, television match official Jim Yuille ruled that the grounding was inconclusive as the Glasgow forwards battled to up the big New Zealander over the whitewash.
Bennett fared better at the hands of the TMO five minutes later as his try was awarded despite replays suggesting that the ball had slipped from his hands under pressure from Court's last-ditch tackle.
The try was allowed to stand and Russell gratefully converted to establish the unassailable 18-point lead for Gregor Townsend's charges.
Ulster battled on until the final whistle but with knocks to Court and Fitzpatrick adding both props to an already over-crowded treatment room, they will need to regroup in time for the Ravenhill showdown with Leinster in two weeks' time.