Juan Uribe hit a two-run homer in the bottom of the eighth inning to reclaim the lead for the Dodgers, who jumped out to an early 2-0 advantage after a pair of Carl Crawford home runs before squandering it with poor defense and a shaky performance by reliever Ronald Belisario.
Kershaw exited after six innings and 91 pitches and gave way to Belisario, who allowed a one-out triple to Elliot Johnson in the seventh.
Braves manager Fredi Gonzalez called upon Jose Constanza to pinch-hit for Garcia, and the reserve infielder delivered an RBI single to give Atlanta its first lead, 3-2.
The Dodgers failed to capitalize on a scoring threat against Braves reliever Luis Avilan in the bottom of the seventh, but Yasiel Puig led off the eighth with a double, setting the stage for Uribe. The veteran infielder failed to lay down a couple of bunts, but jumped all over a 2-2 pitch from David Carpenter and drilled it into the left field seats.
Dodgers closer Kenley Jansen struck out the side in the ninth inning to preserve the victory.
Los Angeles became the first team to advance to the LCS.