The Dodgers salvaged a split of a doubleheader after the Nationals had won the opener 3-1.
Washington's lead over Atlanta in the National League East was reduced to five games.
Los Angeles built a 6-0 cushion through seven innings and had that entire advantage wiped out in the eighth.
Michael Morse drove in three runs during Washington's big inning, hitting a solo homer in his first at-bat and then producing a two-run single that tied the contest in his second trip to the plate.
Washington's rally, however, was wasted when Kemp hit his 19th homer of the season against Tyler Clippard (2-5) leading off the ninth.
The final two outs in Washington's six-run inning were recorded by Ronald Belisario (7-1), who wound up getting the victory. Brandon League retired the side in the ninth for his 12th save.
Los Angeles finished the night two games behind St. Louis for the second wild card spot in the National League. The Cardinals kept their two-game lead with a 5-0 win over Houston.
The Dodgers built their 6-0 lead with back-to-back three-run innings. Hanley Ramirez contributed a two-run single in the third and his fielder's choice grounder in the fourth drove in another run.