The loss was the seventh straight for Arizona.
The Dodgers are five games ahead of San Francisco atop the National League West.
Finley hit a solo home run in the fifth inning and a two-run shot in the sixth. Adrian Beltre drove in a run and scored another for the Dodgers.
Jose Lima (12-5) was the winner, giving up four hits and three runs in 6 1/3 innings. Eric Gagne got his 38th save.
Edgar Gonzalez (0-9) was the losing pitcher.
2014: The Year in Music [PHOTOS]