But despite a late rally from Glasgow, who had to settle for a losing bonus point, the Scarlets held on for their fifth Magners League victory of the season.
Nigel Davies' charges went into the game without seven frontline players, including the likes of new Wales captain Matthew Rees, Stephen Jones, David Lyons, Sean Lamont, Tavis Knoyle, Jon Davies and George North.
But they more than held their own during a first half played out in torrential rain, with the likes of youngsters Nic Reynolds on the left wing and number 8 Ben Morgan stepping up.
Fly-half Rhys Priestland had much the better of the conditions compared to his opposite number Ruaridh Jackson, who missed both of his first half penalty shots.
On the other hand Priestland found the target with four out of his five penalty attempts as the Scarlets took a 12-0 lead into half-time.
Priestland's first effort came after just seven minutes, with the Scarlets going through the phases despite the wet conditions.
He doubled the lead with a 17th-minute penalty before the Scarlets finished the half much the stronger, with the Warriors full-back Peter Horne struggling under the high ball.
Glasgow were not helped by the loss of skipper John Barclay to the sin-bin after he kicked the ball out of a ruck. It allowed Priestland to put over two more penalties in the 35th and 37th minutes.
The Scarlets began the second half well enough, with Priestland successful with a 47th minute kick to extend the hosts' advantage to 15-0.
But the sin-binning of lock Lou Reed for a professional foul proved crucial, inviting Glasgow back into the game. They scored two converted tries in the space of four minutes to get right back in touch.
Not only were the Scarlets reduced to 14 men but their defence disappeared as replacement Weir skipped past two tackles for the first try.
And Glasgow got back to within one point when Max Evans broke through and put Van der Merwe over for the second try to send a bit of panic into Scarlet ranks.
But they were given some respite when Glasgow were penalised for being in front of the kicker and Priestland converted his sixth and final kick to decide it.
|Scarlets Score Card|
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|