Leigh Halfpenny kicked five penalties and converted two second-half tries by Rhys Patchell and Scott Williams after La Rochelle had taken the lead thanks to Romain Sazy's early try with Alexi Bales adding a conversion and a penalty. Benjamin Noble also added a conversion, while Pierre Boudehent scored a late try for La Rochelle.
The visitors were repeatedly sanctioned and failed to score despite dominating a long spell in the second half.
Scarlets will take on either champions Leinster or Saracens, the sole English survivors in the competition, for a place in the final.
La Rochelle put pressure on the hosts with some clever kicking early on and it paid off when Sazy touched down after the Scarlets mishandled Jeremy Sinzelle's kick.
But the visitors lacked discipline and they were trailing by five points midway through the first half after four penalties by Halfpenny.
La Rochelle suffered a heavy blow when key flanker Levani Botia had to be replaced with a knee injury by France international Kevin Gourdon.
Bales's penalty on the stroke of halftime put La Rochelle within two points of Scarlets, only for Halfpenny to restore a five-point advantage with another three-pointer.
Scarlets weathered a strong storm before the hour as La Rochelle piled on the pressure and it proved to be the turning point.
Shortly afterwards, Patchell dived over after Hadleigh Parkes had pierced through the La Rochelle defence.
Scarlets played most of the last 10 minutes with 14 men after Will Boyde was shown a yellow card, but their opponents were worn down and the Welsh wrapped it up effectively when Williams scored their second try at the end of an impressive run.
La Rochelle scored a consolation try after the buzzer.
(Reporting by Julien Pretot; editing by Pritha Sarkar)
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