The Dodgers produced all their runs in the final three innings, two of them coming in during the seventh on a throwing error by Florida shortstop Hanley Ramirez.
Los Angeles took a 4-1 lead in the seventh and added three more in the ninth thanks in part to a two-run double by James Loney.
Manny Ramirez went 2-for-5 with an RBI and a run scored for the Dodgers.
Hiroki Kuroda (1-0) allowed an unearned run in eight innings to get the victory. He struck out seven.
Starter Chris Volstad (0-1) went 6 1/3 innings in the loss, surrendering three runs on five hits.
2014: The Year in Music [PHOTOS]