Kershaw, the National League's earned run average leader in each of the last two seasons, gave up a run on three hits and struck out 12. He threw 124 pitches before being lifted for a pinch-hitter in the eighth.
Adrian Gonzalez hit a two-run homer to highlight the Los Angeles attack and the Dodgers seized home-field advantage in the best-of-five National League Division Series.
Atlanta will host Game 2 on Friday before the series moves to Los Angeles for the third game on Sunday.
The home run by Gonzalez came with two outs in the third and followed an infield single by Carl Crawford.
Kris Medlen, who won 15 games in the regular season and had not lost since Aug. 23, gave up five runs on nine hits in just four innings.