Kemp hit a two-run blast as part of a three-run first and Cruz delivered a two-run shot in the third.
That helped the Dodgers build a 6-2 advantage, but the Mets made a game of it with the assistance of two unearned runs.
A two-run homer by Jordany Valdespin in the seventh brought the Mets within one, but LA relievers Ronald Belisario and Kenley Jansen shut down New York over the final two innings.
Aaron Harang (7-5) worked five innings for the win. He gave up two runs, one earned, on four hits over five innings.
Johan Santana (6-7) lasted only three frames while taking the loss. He allowed six runs on seven hits.
2014: The Year in Music [PHOTOS]