It was a frustrating evening from the off for Glasgow, whose other defeat away from home in the Guinness Pro12 came at the hands of Cardiff Blues in October.
Gregor Townsend’s men entered the game in good form having won their last three matches to keep tabs at the top of the table with Leinster and the Ospreys.
But two second-half yellow cards for Pat MacArthur and Brian Alainu’uese paved the way for the Scarlets to wreak havoc in a dominant second half with Will Boyde scoring a brace of tries each side of the interval for the Wales side.
Glasgow did have a healthy amount of possession early on but that was to no reward courtesy of a combination of mistakes and a resolute Scarlets defence.
Peter Horne was at the heart of Warriors plays but he, Mark Bennett and Rory Hughes, in particular, couldn’t find a way through.
And, against the run of the play, the Scarlets found the opening score with a dazzling team effort that spanned from their own 22.
James Davies made the original break after he carved a hole in the Warriors’ defence before finding Jonathan Evans, who made his way into the Glasgow half. The ball recycled its way to DTH van der Merwe on the wing who was able to brush off a number of tackles. Steffan Evans wriggled his way through before offloading to Boyde who managed to battle his way over.
Mark Bennett knocked a penalty wide from 40 metres as the Warriors looked for an immediate response.
Scarlets prop Wyn Jones was sent to the bin by referee Gary Conway for pulling down the maul as Glasgow came knocking once more, but the Scarlets halted the resulting lineout and were able to clear their lines; it turned out to be that kind of evening for the lacklustre Warriors.
Horne took over the tee from Bennett and put Glasgow on the board with a penalty after Scarlets were caught not releasing. But the 20-cap Scotland stand-off, who was released from Scotland’s squad to play Australia next weekend, squandered a chance for another three points as he sliced the ball wide.
Bennett thought he had a chance when he picked off a loose pass from Rio Team GB colleague Davies late in the half, only for the referee to blow a stop to the play.
Glasgow’s misery soon got worse when the Scarlets scored two early second-half tries each side of hooker MacArthur’s yellow card.
First, Patchell found some space at the halfway line before finding wing Evans who secured his second assist of the game after he skipped his way through the Warriors and found scrum-half Jonathan Evans who crossed at the posts.
MacArthur departed for a high tackle ten minutes later with Patchell scoring the resulting penalty to pull the Scarlets further ahead.
And Boyde was able to force his way over for his second after a commanding Scarlets driving maul to leave a bitter taste among the Warriors camp.
It just wasn’t their day and that was capped off when Alainu’use was yellow carded for an off-the-ball incident.
Glasgow worked their way into Scarlets territory and threatened a late try but that was soon dashed when an inspired Scarlets defence held firm to quash any danger. The Welsh side closed the game out fairly comfortably for their fifth successive Pro12 win as they continue to charge up the table.