Greinke started and was limited to five innings, allowing two hits, walking one and striking out three.
J.P. Howell (4-1) earned the decision with Chris Withrow and Kenley Jansen helping complete the two-hit shutout. Jansen logged his 27th save.
National League West champion Los Angeles scored the game's only run in the seventh inning when Michael Young belted a two-out double over Will Venable's head in right field and Adrian Gonzalez scored on Venable's error.
San Diego's Andrew Cashner (10-9) lost despite striking out seven in seven innings. He yielded just the one unearned run on four hits.
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance
Wisconsin business offering 'therapeutic cuddling' forced to close