Ellis socked a solo shot in the third inning and put the Dodgers ahead 3-1 with an RBI single in the fifth.
The Los Angeles catcher capped his big night with a solo blast in the seventh, finishing with three RBI as the Dodgers took the opener of a three-game series.
Hanley Ramirez went 2-for-4 with two RBI for Los Angeles.
Chad Billingsley (7-9) won his third straight start, holding the Cubs to one run on four hits over seven innings. The right-hander walked two and struck out seven.
The victory enabled the second-place Dodgers to stay one-half game behind National League West-leading San Francisco following the Giants' triumph over Colorado Friday.
Chicago's Jeff Samardzija (7-9) was tagged for five runs on eight hits over 5 1/3 frames.
Luis Valbuena delivered the Cubs' only RBI.