The Kings snapped a two-game losing streak and cooled off the Blues with a four-goal second period. St. Louis had won four of its previous five.
Cloutier, getting a rare start, made 32 saves. In his last start, Feb. 7, he gave up three goals on 21 shots before being lifted. He had a shutout working Thursday night until Martin Rucinsky scored on the power play with 4:02 remaining in the third period.
Anze Kopitar opened the scoring with a power-play goal 6:43 into the second and Frolov then produced two goals in a span of 2:44 to make it a 3-0 game.
Frolov completed his hat trick with a wrister 3:31 into the third period.
St. Louis' Manny Legace was removed after allowing four goals on 15 shots. Chris Beckford-Tseu surrendered the other Los Angeles goal.