Kershaw (13-10) nearly went the distance, carrying a two-hitter after eight innings. He ran into some trouble in the ninth, allowing the first two hitters to reach before exiting, and ended up giving up four hits and one run while fanning nine without walking a batter.
Reed Johnson added a homer, while Trent Oeltjen hit an RBI triple in the victory, only the Dodgers' third in nine games.
The Diamondbacks, coming off a three-game sweep of the playoff hopeful Rockies, managed just three other baserunners aside from Kelly Johnson's two singles. Barry Enright (6-6) was dealt the hard-luck loss -- his fourth straight -- after lasting eight innings and giving up two runs, five hits and a walk.
The Dodgers produced all the offense they needed with a a run apiece in the third and fourth.
A.J. Ellis worked a leadoff walk off Enright, though the next two hitters were retired without a problem. Oeltjen, however, tripled to right to put the first run on the board.
Los Angeles added a run in the fourth when Andre Ethier tripled leading off and came around to score on Jay Gibbons' sacrifice fly.
Kershaw did the rest.
The lanky lefty set down the first 11 hitters he faced, striking out five, until Kelly Johnson singled with two away in the fourth. Mark Reynolds flied out to end the frame, and Kershaw struck out the first two batters of the fifth before John Hester reached on an error.
The miscue didn't affect the score, however, as Kershaw induced a pop out from Cole Gillespie to keep Arizona off the board.
After a perfect sixth, Kelly Johnson notched the Diamondbacks' second hit with a leadoff single in the seventh. Kershaw, though, retired the next three hitters, including two via strikeout.
Kershaw tossed a perfect eighth, and Reed Johnson homered in the ninth to add an insurance run. Arizona finally got its offense going in the ninth, as Chris Young singled leading off and scored on Tony Abreu's double.
Kenley Jansen came in from the bullpen and got Kelly Johnson to pop out, but walked Stephen Drew. He came back to strike out both Adam LaRoche and Ryan Church to end the game and earn his second save.
The Dodgers have dominated the season series, 11-2...The Diamondbacks had a four-game home win streak snapped...Kershaw lowered his earned run average to 2.91...Game time: 2:26.