The teams scored two tries apiece in difficult conditions and while the visitors had their opportunities, they failed to capitalise on a number of occasions, which ended up costing them.
The Cell C Sharks will rue the fact that too many errors ended up costing them momentum, as they had the upper hand in terms of territory and possession, while the Scarlets were also penalised more.
However, the Scarlets probably adapted better to the conditions on their home turf, using their tactical kicking to good effect while punishing the visitors' ill-discipline.
Springbok captain Siya Kolisi and Welsh speedster Steff Evans scored the only tries of the first half, which was quite tight as the only difference between the teams was two penalty goals by Costelow.
Costelow added four more penalty goals after the break, while Evans got his second five-pointer and Bongi Mbonambi went over for the Cell C Sharks' second try.
When Curwin Bosch converted the Bok hooker's try, it was a six-point game, but Costelow had the final say with two more penalty goals to give his team a great win in front of their home fans.
Scarlets 32 (13) - Tries: Steff Evans (2). Conversions: Sam Costelow (2). Penalty goals: Costelow (6).
Cell C Sharks 20 (7) - Tries: Siya Kolisi, Bongi Mbonambi. Conversions: Curwin Bosch (2). Penalty goals: Bosch (2).