Finn Russell outscored Aled Thomas as Glasgow came away with a scrappy 9-6 win over the Scarlets in poor conditions.
Torrential rain throughout the night saw both sides make a large number of handling errors, which meant the game would have to be decided from the tee.
Despite the appalling weather, Russell slotted his first attempt at the posts after four minutes from 22 metres out to open the scoring.
Aled Thomas' first kick failed to level the scores, as his kick got caught in the wind and was dragged wide of the uprights.
The Welsh side then went down to 14 men as Thomas was shown to the sin bin after being adjudged to have deliberately knocked the ball on, which allowed Russell to extend Glasgow's lead to six.
To round off the first half Russell took aim for a third time, but this time his kick flew low and wide in Llanelli's driving wind and rain.
Five minutes in to the second half and yet another score comes from the boot of Russell, taking Glasgow's winning margin up to nine points.
Thomas made amends for his earlier miss, and opened Scarlets' account in the game after Sean Lamont made his way to the sin-bin for another intentional knock on.
A harsh call from referee Pascal Gauzere saw Glasgow Warriors go down to 13 men as Simone Favaro was sent to the sin-bin as he attempted to charge down a clearance from the boot of Aled Thomas, and was ruled to be late by the French official.
Scarlets' third penalty kick saw Thomas convert his second penalty of the game, bringing the Welsh side within a score of the Scottish side.
A try-less night at Parc y Scarlets failed to see the current PRO12 leaders get off the bottom of Pool 3, after gaining just two bonus points from their four fixtures so far.
The win means Glasgow's hopes of qualifying for the knockout rounds are still alive, as they sit just one point behind Northampton Saints with a game in hand.
Pens: Thomas 2
Yellow Card: Thomas
For Glasgow Warriors:
Pens: Russell 3
Yellow Cards: Lamont, Favaro
Scarlets: 15 Mike Collins, 14 Steff Evans, 13 Gareth Owen, 12 Hadleigh Parkes, 11 DTH van der Merwe, 10 Aled Thomas, 9 Gareth Davies, 8 Morgan Allen, 7 Jack Condy, 6 Lewis Rawlins, 5 Maselino Paulino, 4 Jake Ball, 3 Samson Lee, 2 Emyr Phillips (c), 1 Rob Evans
Replacements: 16 Ken Owens, 17 Wyn Jones, 18 Rhodri Jones, 19 George Earle, 20 Tom Price, 21 Aled Davies, 22 Steven Shingler, 23 Harry Robinson
Glasgow Warriors: 15 Tommy Seymour, 14 Taqele Naiyaravoro, 13 Mark Bennett, 12 Alex Dunbar, 11 Sean Lamont, 10 Finn Russell, 9 Mike Blair, 8 Josh Strauss, 7 Simone Favaro, 6. Robert Harley, 5 Jonny Gray (c), 4 Leone Nakarawa, 3 Sila Puafisi, 2 Fraser Brown, 1 Alex Allan
Replacements: 16 Shalva Mamukashvili, 17 Gordon Reid, 18 Zander Fagerson, 19 Tim Swinson, 20 Ryan Wilson, 21 Grayson Hart, 22 Duncan Weir, 23 Lee Jones
Referee: Pascal Gauzère (France)
Assistant Referees: Maxime Chalon (France), Jean-Luc Rebollal (France)
TMO: Bruno Bessot (France)