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.
Celebrity Breakups and divorces of 2014 [PHOTOS]