After going into the break down by two points, Ulster went in front through David McCann only to be pegged back again by the away side just minutes later. Replacement scrum-half, Dave Shanahan, had the final say of the match, with his late winner making the difference on the scoreline.
Richie Murphy's men began the season with two debutants in the starting XV, with prop, Corrie Barrett, and fly-half, Aidan Morgan, getting their first starts.
James McCormick and Werner Kok would also get their first appearances from the bench in the second half.
There was a welcome return to the team for captain Iain Henderson, who hadn't played since April.
Franco Smith's champions got off to the perfect start, by getting into good territory following Ulster penalties. Their prolific hooker, Johnny Matthews, getting the first score of the match through, you guessed it, a driving maul from a lineout. Jordan's kick was wide, leaving the score at 0-5.
A Nathan Doak penalty then narrowed the score to two after a period of Ulster pressure in the Glasgow 22.
Then, Aidan Morgan, made the best possible contribution to impress the home crowd. The Kiwi fly-half showed great anticipation to charge down Tom Jordan's kick in his own 22, kicking it downfield. Mike Lowry kept the ball alive and Morgan ran a great line, diving over for a debut try to give Ulster the lead. Nathan Doak slotted home the conversion for a 10-5 lead.
The away side would then take back the lead before half-time, after Henco Venter scored from close range and Jordan converted to make the scoreline 10-12 going into the interval.
Glasgow started the second half off strongly, and were picking up early pens to gain good field position.
Their forward pack were also beginning to get a bit of second-half joy at scrum-time.
Murphy opted for fresh reinforcements with Andrew Warwick and Tom O'Toole, who came on to shore up the set piece.
The away side thought they had scored a slick try through flanker, Rory Darge, on the left wing, however as Ulster fans protested, a TMO check confirmed the crowd's suspicion that a forward pass had been made in the build-up.
There was a turning point in the game when Stewart Moore was tackled high at a ruck, forcing him off and giving the referee a TMO check. The result was that Tom Jordan was sent to the bin and Ulster piled the pressure on.
The Glaswegians were even reduced to 13 after a series of penalties in the Glasgow 22 that saw Richie Gray receive his marching orders.
Hooker, James McCormick, and wing, Werner Kok, were sent on for their debuts, and both made great contributions in the drive towards the finish.
After a dominant spell of Ulster pressure, the stubborn Scottish defence caved after flanker, David McCann, reached over a pile of bodies in the ruck on the Glasgow tryline for a vital score. The conversion couldn't be added from Morgan.
The try felt like a relief after the second half onsalught, however Glasgow punctured the good mood almost straight away from the restart.
Their skipper, Kyle Steyn, racing over the Ulster whitewash after some great interplay with Darge and Ferrie on the right wing. The conversion was scored to give the the away side a four point lead with minutes on the clock.
Not to be beaten, Ulster rallied for a late turnaround.
With Ulster being roared on towards the Glasgow tryline, some huge carries got the home team just inches out and replacement scrum-half, Dave Shanahan, was the hero of the night, picking and going to squeeze through the slightest of gaps for the match-winning score.
Every Ulster supporter held their breath as a TMO check was made to see if Shanahan had knocked on but the try was good and the crowd roared with the referee's signal.
Ulster had been banging on the door for most of the second half and the crowd were vital in helping the team over the line for a memorable way to start to season.
Ulster now turn their attention to South Africa for a mini-tour facing the Emirates Lions and Vodacom Bulls over the next two weekends.
Scorers
Ulster:
TRY: Morgan, McCann, Shanahan
CON: Doak
PEN: Doak
Glasgow Warriors:
TRY: Matthews, Venter, Steyn
CON: Jordan x2
Teams
Ulster:
(15-9) Ethan McIlroy, Mike Lowry, Stewart Moore, Jude Postlethwaite, Jacob Stockdale, Aidan Morgan, Nathan Doak;
(1-8) Eric O’Sullivan, John Andrew, Corrie Barrett, Iain Henderson (C), Kieran Treadwell, James McNabney, David McCann, Nick Timoney.
Replacements: James McCormick, Andrew Warwick, Tom O’Toole, Harry Sheridan, Cormac Izuchukwu, Dave Shanahan, James Humphreys, Werner Kok.
Glasgow Warriors:
(15-9) McKay; Cancelliere, McDowall, Tuipulotu, Steyn (C); Jordan, Dobie;
(1-8) Bhatti, Matthews, Talakai; Williamson, Gray; M Fagerson, Darge, Venter.
Replacements: Hiddleston, McBeth, Z Fagerson, Samuel, Brown, Ferrie, Afshar, Hastings.
