The Scarlets, last season’s title winners, conceded seven tries in what was their heaviest defeat in the history of the competition.
Glasgow opened the scoring in a free-flowing opening period through Steve Swindall when he went over from short range and the Lamont brothers were soon also on the scoresheet.
Sean Lamont´s score saw him outpace Tal Selley over 95 metres after an interception when the Glasgow defence had looked stretched.
Aisea Havili got on the end of some good work from Chris Wyatt to cross, before Tal Selley raced in to score and lock Vernon Cooper forced his way over on the stroke of half-time.But the Scarlets were not at the races after the break and were duly put to the sword by their visitors.
Their lacklustre display was summed up when Gareth Bowen´s attempted kick to touch from a penalty was caught by Sam Pinder, who collected the ball and raced 90 metres,eventually dotting down underneath the posts.
The Scarlets rallied late on to claim a bonus point through tries from Barry Davies and Havili, but it was too little too late.