Rhys Priestland kicked all of Bath's points as Todd Blackadder's side ground out an 18-13 win at the Scarlets to make it two wins from two in the Champions Cup.
The Premiership outfit had cruised to a 23-0 success over Treviso last time out, but were faced with an altogether sterner test at a rain-lashed Parc y Scarlets on Friday.
The first two of Priestland's six penalties sandwiched one from Leigh Halfpenny as Bath led 6-3 after 10 minutes, but it was the home side who scored the game's only try midway through the opening half.
And it was one that defied the slippery conditions as Steff Evans embarked on a searing break and fed Gareth Davies inside him.
Davies was hauled down by Anthony Watson but managed to pop the ball back to Evans, who raced over.
Halfpenny converted but Priestland showcased his own composure from the tee with two more penalties before half-time to give Bath a 12-10 advantage.
That was stretched to 18-10 with 12 minutes remaining as Priestland continued to punish the Scarlets, who could only claim a losing bonus point through Halfpenny's penalty seven minutes from the end.