Billingsley (10-9) continued a hot streak with his sixth victory in six starts, coming up with big outs to strand Atlanta runners on third base twice during the contest.
The right-hander issued a pair of walks and struck out four for the second-place Dodgers, who came into the contest trailing National League West-leading San Francisco by a half-game.
Mark Ellis provided four RBI with a two-run single in the eighth inning and a two-run double in the ninth, while Luis Cruz socked a solo homer for the victors.
Mike Minor (6-10) fell despite allowing just one run on five hits over seven full frames for the NL wild card-leading Braves.
Celebrity Families of 2014 [PHOTOS]