Kershaw (9-6) helped the Dodgers remain a half-game behind first-place San Francisco in the NL West. The reigning NL Cy Young Award winner, coming off a five-hit shutout against the Giants last Sunday, struck out seven and allowed his only run on a fourth-inning double by Alfonso Soriano while lowering his ERA to 2.88.
Chris Volstad's winless streak reached 21 games with Saturday's loss.
Volstad (0-8) yielded two runs and six hits through seven innings before he was lifted for a pinch-hitter. The right-hander is 0-13 with eight no-decisions and a 5.49 ERA since beating Houston 5-4 on July 10 last season with the Marlins, who traded him to the Cubs in January for Carlos Zambrano.
Volstad was recalled from Triple-A Iowa on Wednesday, a day after starters Ryan Dempster and Paul Maholm were dealt away before the non-waiver trade deadline. This is Volstad's third stint with the big club this season, including a 5-1 loss to the Dodgers on May 5 at Wrigley Field.
Soriano's run-scoring double ended an RBI drought of five games and 23 at-bats since his two-run triple against St. Louis' Joe Kelly on July 28 at Chicago.
The Dodgers responded in the bottom of the fourth with Kemp's 16th homer, a towering drive that deflected off center fielder Joe Mather's glove as he attempted a leaping grab in right-center. Kemp is hitting .336 with 13 RBIs in 20 games since coming off the disabled list.
Kershaw walked No. 8 hitter Luis Valbuena his first two times up, and Volstad advanced the runner both times with sacrifice bunts. But Castro grounded out to third to end the third-inning threat, then took a called third strike to end the fourth. The Cubs' leadoff hitter is 0 for 13 against Kershaw.