The back-to-back-to-back solo shots came in a span of four pitches by Braves starter Ben Sheets (4-3). It was the first time the Dodgers have hit three consecutive homers since 2007.
Ramirez added a three-run shot in the sixth to finish with four RBI.
The four homers were the only hits Los Angeles had in the game.
Aaron Harang (9-7) collected the victory, striking out eight over 6 2/3 innings while yielding just one run on four hits. The right-hander overcame five walks.
Kenley Jansen picked up his 25th save for the second-place Dodgers, who came into the contest trailing the San Francisco Giants by one-half game in the National League West.
Sheets surrendered the six runs in six innings.
Martin Prado homered for the National League wild card-leading Braves, whose four-game winning streak was snapped.