Clermont captain Aurelien Rougerie registered the bonus-point try 14 minutes from time, adding to earlier scores from Napolioni Nalaga, Morgan Parra and Benson Stanley.
It was the Scarlets' seventh defeat in eight games in all competitions since the beginning of December.
The Scarlets were much better side in the second half but still failed to break their duck.
Wales wing George North returned for the hosts after suffering a neck injury in the RaboDirect PRO12 defeat against Ulster earlier in the month, but centre Scott Williams missed out with a shoulder injury.
Clermont included former Scarlets Lee Byrne and Jamie Cudmore in their line-up, and Regan King on the bench.
It took Clermont only until the seventh minute to score their first try when Napolioni Nalaga raced away from the line from 25 metres out after good attacking work from fellow wing Julien Malzieu and Benjamin Cudmore. Parra added the extras.
And Nalaga was involved again four minutes later when he was the victim of a high tackle from Scarlets full-back Liam Williams which allowed Parra to kick a penalty from the left touchline.
The Scarlets did not help themselves as Clermont went 17-0 up in as many minutes when Parra took an interception pass from number eight Rob McCusker at the base of a scrum. Parra also converted.
Clermont, who beat the Scarlets 49-16 in the first game in October, enjoyed a wealth of possession in the first half but the third try did not come until the 37th minute when replacement scrum-half Ludovic Radosavljevic - on for the injured Parra - found Stanley with a pinpoint pass.
And the centre went over by the posts for David Skrela to convert, giving the French side a 24-0 interval lead.
The Scarlets got some ball in their hands a bit more at the start of the second half but failed to make any headway as the third quarter remained scoreless.
But former Scarlet King came on and had an immediate impact, giving Rougerie the pass which saw Clermont claim their fourth try and the bonus point on 66 minutes.
The Scarlets did have the chance of a try following a clean break by centre Adam Warren, but Josh Turnbull knocked on going over the line.