The Dodgers bounced back from a loss on Thursday that ended a six-game winning streak. Los Angeles has captured 24 of its last 30 contests.
Kershaw (10-6) went eight innings for the victory, striking out eight and giving up a run on six hits.
Kenley Jansen worked a perfect ninth, striking out two in collecting his 13th save.
The Cincinnati run was singled home by Jay Bruce in the seventh. The Reds had won their previous two games.