Kemp crushed a two-run homer in the second inning, the sound of bat hitting ball reminiscent of the kind of contact he made regularly three seasons ago when he was in the midst of his career year, and was runner-up in the NL MVP vote.
Kershaw went seven innings, allowing one run, eight hits and a walk and striking out seven. He also snapped his somewhat odd streak of having struck out exactly nine in each of four consecutive starts.
Kershaw went into Friday with a 1-5 record in his last eight starts against the Diamondbacks.
The Dodgers' often shaky defense made several nice plays behind him on this night, including back-to-back outstanding plays by second baseman Dee Gordon in the fifth.
It added up to the first career loss for Arizona rookie right-hander Chase Anderson, who was 5-0 in his first five major league starts.
Anderson walked Adrian Gonzalez to open the bottom of the second before Kemp drilled his sixth home run of the season -- his first since May 10.
The Dodgers added one more in the seventh after Hanley Ramirez, back in the lineup after missing three starts with a sore shoulder, led off with a double off reliever Will Harris.
Ramirez took third when Yasiel Puig bounced out to first and scored when Gonzalez lined a single to right.
The Dodgers added what would hold up as the decisive run in the eighth after A.J. Ellis led off with a single against right-hander Evan Marshall. He took second on a sacrifice bunt by Chone Figgins before pinch-hitter Justin Turner singled to center.
Third base coach Lorenzo Bundy tried to stop Ellis at third [corrected] -- who was just off the disabled list and coming off a sprained ankle -- but not wanting to put on the brakes, he ran through the stop sign and scored what proved the winning run when the throw went wide of the plate.
Brian Wilson, who had not given up a run in his previous 10 appearances, allowed the Diamondbacks to pull within one after he took over to start the eighth. A leadoff infield hit by Hill and a single by Martin Prado preceded a run-scoring basehit by catcher Tuffy Gosewisch.
Dodgers Manager Don Mattingly had seen enough and pulled Wilson in favor of left-hander J.P. Howell, who struck out David Peralta and got pinch-hitter Miguel Montero to fly out to center fielder Andre Ethier at the warning track for the inning’s final two outs.
Kenley Jansen gave up one run on a pair of singles and a walk in the ninth, but held on to earn his 18th save.
The Dodgers are now 9-3 on the season against the Diamondbacks, but 27-30 against everyone else.