The home side took the lead in the Heineken Cup Pool Four match through two early penalties from Brock James, before returning Welsh international Rhys Priestland pulled the visitors back to 6-3 and shaved a post three minutes before the break.
Clermont dominated a scrappy first half, and looked to have scored twice when Napolioni Nalaga and Thomas Domingo seemed to cross the line, but their power was matched by resilient defence and it remained 6-3 going into the break.
The Scarlets resistance was finally broken early in the second half when Canadian lock Jamie Cudmore, who spent three years at the west Wales club, drove over for the first try of the game. Brock James added the conversion.
Jordan Williams put the visitors back in touch at 13-6 with a superb penalty from the halfway line, but the power of the home side began to tell and Fijian wing Nalaga raced away for two tries in quick succession to put the game out of sight.
Spotting space behind, James chipped a cross-kick into the corner, which bounced favourably for Nalaga to collect his first try and score acrobatically. James was once again on target with the conversion and Clermont quickly put the result beyond doubt when Nalaga scorched over for a second time.
They ran riot in the build-up, with Regan King and Aurelien Rougerie causing the visitors major problems, but it was the deft inside pass from Nathan Hines that created the opening.
The Scottish veteran released Sitiveni Sivivatu and the former All Black bamboozled Jordan Williams before sending Nalaga over the whitewash.
All that was left for the home side was to finish off with a bonus point, but it did not look as though it was going to emerge.
Scarlets' latest Welsh international Rhodri Williams scampered over for a consolation try for the Scarlets after 78 minutes and it was not until the fifth minute of injury time that the home fans were able to celebrate a full house of points.
The fourth try for last season's Heineken Cup runners-up came from replacement prop Clement Ric and Mike Delany's conversion made the scoreline look far more comfortable than the contest actually was. The two teams meet again next weekend at Parc y Scarlets.
Scarlets face an uphill fight now to reach the quarter-finals, with an away trip to Racing Metro 92 to come in the new year.