Madison Bumgarner homered off Kershaw and once again outpitched the reigning NL MVP and Cy Young winner, as the Giants shut out the Dodgers for the third straight day, 4-0 Thursday.
The Dodgers have scored a grand total of two runs over their past five games and have been held scoreless for 31 straight innings.
"I actually thought we had some good at-bats throughout the game," Dodgers manager Don Mattingly said. "We felt like we got a lot of guys out there and we made Madison work but we weren't able to get the hits to push across any runs. It was actually not too bad."
San Francisco outscored the Dodgers 10-0 in sweeping the three-game series. The champion Giants have won six in a row overall.
"You don't think you'll come here and not score a run for three games," Mattingly said. "If you're getting good pitches to hit, and you're not chasing anything up there, you're having good at bats."
Kershaw acknowledged being a little bit frustrated but said he could have pitched better.
"I didn't feel like I had the best stuff," he said. "I just tried to make it work. I got some outs. That last inning got away from me, which was really tough. Pitch against a guy like that, and one or two runs are valuable."
This was the third time this season that Bumgarner, the current World Series MVP, had started against Kershaw — the Giants have won all three.
Bumgarner became the first pitcher to homer off Kershaw (2-3). The Giants' star connected for his seventh career home run, hitting a solo shot into the left field bleachers in the third.
Last year, Bumgarner hit four home runs, including two grand slams. He had managed just one single in 17 at-bats this year going into the game.
"The Giants beat us, plain and simple," Los Angeles catcher A.J. Ellis said. "They played better. We have to regroup. This is not the way Dodgers play. We're going home and we play better there."
The Dodgers are 4-5 in games started by Kershaw this season after losing just four of his 27 starts last year.
"I'm sure he's frustrated," Mattingly said. "He's pitching good enough to win but we don't get him enough runs. It's frustrating for all of us."
The Giants have won all six games between the teams at AT&T Park this year, matching their longest home winning streak against Los Angeles in 41 years.
Kershaw allowed four runs on seven hits and two walks in 7 1-3 innings. He has a 4.32 ERA this year.
Kershaw lost for the third time in 13 starts in San Francisco. He entered the game with a career 0.97 ERA at the Giants' park.
"Clayton was under control the whole game," Ellis said. "He did a nice job piecing his way through the game. He really cruised."
Mattingly said it was a matter of continuing to produce solid at-bats.
"We just have to continue to do what we're doing," he said. "The runs will come. I'm still not worried. We're not going to panic and we're going to be fine. We hit a little stretch and we're still in good position."
Dodgers: LHP Hyun-Jin Ryu underwent surgery on his left shoulder and will not pitch the rest of the season. Manager Don Mattingly said the surgery "went as well as could be expected." He also expects Ryu to be ready to pitch again by spring training.
Dodgers: RHP Zack Greinke (5-1, 1.52) will start Friday against the San Diego Padres. Greinke is coming off his first loss but the Padres are a perfect foil for him. He's 5-0 with a 1.58 ERA in nine career starts against them. He's allowed one earned run in 13 innings against the Padres this year.