Kemp had four hits for the Dodgers, who clinched a playoff berth on Friday and entered with a 3 1-2 game lead over the Giants in the NL West. Los Angeles pushed starter Dan Haren back a day so he could face San Francisco on Monday.
The Dodgers instead used the bullpen. Jamey Wright made his first start since Sept. 1, 2013, with the Rays, allowing a run and three hits in two innings.
Welington Castillo homered for the last-place Cubs, who pulled within a run in the fifth. The Dodgers had 16 hits, and the teams combined for 59 runs during the four-game series.
Jacob Turner (5-11) allowed five runs in five innings in his fifth start for the Cubs since he was acquired from Miami on Aug. 8 for two Class-A pitchers.
Kemp's two-run home run - his 23rd - extended the Dodgers' lead to 4-1 in the third. Arismendy Alcantara's RBI double pulled the Cubs to 4-2 in the bottom of the inning.
Puig remained in the game after an awkward slide in the fifth. His right foot appeared to catch in the dirt and he stopped short of the bag. After the trainer checked on him, Puig scored from second on Kemp's single for a 5-2 lead.