Tries from Ken Owens and Liam Williams saw Scarlets win 29-6 over the Warriors at Parc Y Scarlets in Llanelli and continue their push for the RaboDirect PRO12 play-off place.
It was a very disappointing display from Gregor Townsend's side as they were also knocked off the top of the table by Ulster, and they must now pick themselves up for their final scheduled home game against Ospreys next Friday at Scotstoun.
The Warriors were never really at the races and inspired by the excellent kicking off Owen Williams the Scarlets moved up to fourth in the league, with Ospreys playing Treviso tomorrow.
In the third minute a clever move saw Liam Williams release Jonathan Davies down the right and the scrambling Glasgow defence was forced to concede a penalty.
Fly-half Owen Williams, who has appeared in the last six games for the Welsh region, boomed over the long-range kick and the Scarlets were 3-0 up.
The Warriors were really struggling to settle in the opening exchanges, Ruaridh Jackson's kick charged down while Peter Horne's pass went straight into touch.
But despite the dominant territory the Warriors defence, so impressive all season long, held firm in the face of some considerable pressure.
But in the 13th minute Gordon Reid used his hands in the ruck and Williams slotted his second penalty of the night.
Ken Owens then broke into the 22 and after a series of pick and go drives around the fringes it was Owens again who burrowed under the posts for the first try of the game, Williams adding the extras for 13-0 after 18 minutes.
Owen Williams then slotted a drop goal from close range before a second Jackson penalty made it 16-6 on the half-hour mark and it stayed that way unti half-time.
Three minutes after the interval and Owen Williams kicked a penalty wide to the relief of the Warriors.
But their stay of execution did not last long as Liam Williams ghosted over for the Scarlets' second try moments later, collecting George North's offload for a a score which Owen Williams' converted to make it 23-6.
A 51st minute penalty from Owen Williams increased that lead to 26-6 and when Duncan Weir, on as a replacement for Jackson, smashed a penalty against the post the Warriors challenge was all but over.
On the hour mark the Scarlets opted for the posts again rather than the corner and Owen Williams continued to impress, slotting another penalty to make it 29-6.
The final quarter of an hour was a somewhat flat affair as both sides appeared to have settled for result before Andy Fenby made a clean break with three minutes remaining but his offload went to ground and the chance was lost.
Gareth Davies came even closer in the dying moments of the game but a fantastic covering tackle from Peter Horne denied him and it finished 29-6.
Scarlets: Liam Williams; George North, Jonathan Davies, Scott Williams, Andy Fenby; Owen Williams, Aled Davies, Phil John, Ken Owens, Samson Lee, George Earle, Johan Synman, Aaron Shingler, Rob McCusker (capt), Johnathan Edwards.
Replacements: Matthew Rees, Rhodri Jones, Deacon Manu, Sione Timani, Josh Turnbull, Gareth Davies, Aled Thomas, Gareth Maule.
Glasgow: Stuart Hogg, Sean Maitland, Mark Bennett, Peter Horne, DTH van der Merwe, Ruaridh Jackson, Henry Pyrgos, Gordon Reid, Pat MacArthur, Moray Low, Tom Ryder, Al Kellock (Captain), Josh Strauss, John Barclay, Ryan Wilson.
Replacements: Dougie Hall, Ryan Grant, Ed Kalman, Tim Swinson, Rob Harley, Niko Matawalu, Duncan Weir, Sean Lamont.
Referee: George Clancy (IRFU, 53rd competition game)
Assistant Referees: Neil Hennessy, Jon Mason (both WRU)