Kershaw (5-3) fanned 10 through the first five innings and went on to hold Seattle to three runs on four hits and two walks.
The reigning National League Cy Young Award winner broke a personal three-game winless streak, throwing 75 of his 115 pitches for strikes.
Jerry Hairston Jr. went 3-for-4 with five RBI, including a three-run homer in the first inning. Elian Herrera added a run batted in for the National League West-leading Dodgers, who improved to an MLB-best 38-22.
Jason Vargas (7-5) was roughed up for five runs on nine hits through six innings for Seattle, which won Friday's series opener 1-0.
Miguel Olivo socked a three-run homer for the Mariners.