Zimmerman (11-8) yielded six hits, walked two and struck out four for National League East-leading Nationals, who improved to 90-57 -- marking the first 90-win season for the franchise since 1993 when they were the Montreal Expos.
Ryan Matthues, Sean Burnett and Drew Storen combined for two scoreless relief innings and Tyler Clippard notched nailed down his 32nd save as the Nats took the rain-delayed opening contest of a three-game series.
The Dodgers' Aaron Harang (9-10) absorbed the loss after allowing a pair of runs on seven hits over 4 1/2 frames.
Hanley Ramirez knocked in the only run for Los Angeles, which came into the contest 1 1/2 games behind the St. Louis Cardinals for a NL wild card spot.
Celebrity Families of 2014 [PHOTOS]