Scarlets broke the Warriors' 20 game winning streak at Scotstoun Stadium as the defending Pro12 champions lost 10-16 against the resolute Welsh team.
Glasgow have lost a number of players to the upcoming World Cup and looked a far cry from the team that dominated the Pro12 last season.
The visitors caused the reigning champions plenty of problems in the first half as Aaron Shingler opened the scoring with a try in the first four minutes.
Hadleigh Parkes got the second 15 minutes later and after three misses Daniel Jones opened his account for the season with a penalty in front of the posts to leave Scralets with a healthy 0-13 lead going into half time.
Glasgow started the second half with plenty of intensity as they fought to get themselves back in the game.
Michael Cusack managed to get Glasgow on the score sheet five minutes into the half but it took the home team until 79 minutes before Glenn Bryce could get another past the visitors.
It was a case of too little too late for the champions.
Scarlets hadn't seen victory at Scotstoun for three years and were looking to take the competitions biggest scalp on their opening game of the season. The Welsh side got off to a great start as they pinned the Warriors back in the opening minutes.
After a series of pick and drives from the visitor's pack Shingler reached over a pile of bodies to get the first try of the match after just four minutes. Jones got off to a shaky start from the tee shanking his first conversion attempt.
Regan King juggled the ball as he broke through the Glasgow line and managed to offload the ball to Parkes who snuck into the corner for the visitor's second try of the match. Jones once again fluffed his lines with the conversion attempt to keep the scores at 0-10.
Jones had the chance to add another three points to the visitors lead but once again couldn't dissect the posts as he completed a hat-trick of misses.
Grayson Hart added to Glasgow's woes when he was yellow carded for a dangerous tackle on King.
The Welsh side continued to cause the home team problems eventually earning a penalty right in front of the posts and this time Jones couldn't miss extending his teams lead to 0-13.
Glasgow hit back first in the second half as they dominated possession in the early minutes. The champions threw wave after wave of attack at the Scarlets defence eventually opening up a gap for Cusack to drive through in the corner.
Wight continued the games trend of missed conversions to leave the scores at 5-13.
Glasgow were penalized for going off their feet and Jones managed to steady the ship for the visitors with three points after a shaky start to the half. Rob Evans was sent to the bin after a series of infringements at the scrum as Glasgow desperately tried to grind more points out of their dominant second half performance.
The Warriors continued to punch holes through a tired Scarlets defence eventually finding a second try through Bryce on the wing on 79 minutes, Rory Clegg shanked the conversion.
James Davies was shown yellow in the lead up to the try giving Glasgow a chance to steal the win with seconds left in the match.
The champions continued to hold onto the ball well after the 80 minute mark, and Scarlets were shown yet another yellow when John Barclay killed the ball on the floor. The home team fought back admirably after a poor first half but left it too little too late as Scarlets managed to cling onto an impressive win.
Tries: Cusack, G. Bryce
Yellow card: Hart
Tries: Shingler, Parkes
Pens: Jones 2
Yellow cards: Evans, J. Davies, Barclay
Glasgow: 15 Glenn Bryce, 14 Lee Jones, 13 Peter Murchie (c), 12 Fraser Lyle, 11 Rory Hughes, 10 Scott Wight, 9 Grayson Hart, 8 Adam Ashe, 7 Chris Fusaro, 6 Josh Strauss, 5 Scott Cummings, 4 Rob Harley, 3 Mike Cusack, 2 Pat MacArthur, 1 Jerry Yanuyanutawa.
Replacements: 16 Kevin Bryce, 17 Alex Allan, 18 Zander Fagerson, 19 Kieran Low, 20 Tyrone Holmes, 21 Mike Blair, 22 Rory Clegg, 23 Robbie Fergusson.
Scarlets: 15 Steffan Evans, 14 Hadleigh Parkes (c), 13 Regan King, 12 Gareth Owen, 11 Michael Tagicakibau, 10 Daniel Jones, 9 Aled Davies, 8 John Barclay, 7 James Davies, 6 Aaron Shingler, 5 Lewis Rawlins, 4 Tom Price, 3 Peter Edwards, 2 Emyr Phillips, 1 Phil John.
Replacements: 16 Kirby Myhill, 17 Rob Evans, 18 Will Taylor, 19 George Earle, 20 Rory Pitman, 21 Rhodri Williams, 22 Aled Thomas, 23 Tom Williams.