The Reds beat the Cardinals earlier on Tuesday to keep the Dodgers alive in the National League Wild Card race for another few hours, but the Dodgers fell behind by three runs and couldn't top the Giants.
Kershaw has been dealing with a hip impingement but tossed eight shutout innings on Friday while striking out 10. He hasn't allowed more than two runs in any of his last seven starts.
"He wouldn't be able to do the things he's doing," Dodgers manager Don Mattingly said on whether Kershaw has been playing with pain. "He couldn't throw. He couldn't actually go out there and play catch."
Kershaw is 7-4 with a 1.39 ERA in 16 career appearances (15 starts) against the Giants. He is 1-3 with a 1.74 ERA in four starts against them this season.
Giants manager Bruce Bochy said before Tuesday's game that he wants to play his regulars on Wednesday whether the Giants won or lost on Tuesday. The Giants will start the NL Division Series on Saturday.
"You really don't like two days off," Bochy said. "It's important that these guys play."
Right-hander Ryan Vogelsong gets the ball for the Giants. After a seven-start stretch in which he allowed 34 earned runs in 29 2/3 innings, Vogelsong has allowed one earned run in his last 12 innings.
Against the Dodgers this season, Vogelsong is 2-1 with a 0.89 ERA.
Giants: Posey not worried about back spasms
Buster Posey started at first base on Tuesday after being removed from Monday's game in the eighth inning with mild back spasms.
Posey went 2-for-4 with an RBI.
"It felt like a crick in my neck, except it was in the upper back," Posey said.
If Posey wasn't dealing with back problems, he could've caught Barry Zito for the eighth time this season. Hector Sanchez has caught Zito 25 times, but Bochy reiterated that he won't hesitate to pair Posey with Zito in the postseason.
Posey is batting .111 (2-for-18) against Kershaw in his career.
Dodgers: Jansen rediscovers better velocity
Reliever Kenley Jensen finally discovered the reason behind the drop in his velocity this season on Saturday against the Rockies.
"Somehow, I just figured it out," Jansen said. "I've been telling everybody I'm not hurt. It turned out I wasn't staying through the ball. It came back to me when I threw a two-seamer."
From pitch one to pitch two to the Rockies' Jonathan Herrera, Jansen's velocity jumped five miles an hour, from 90 to 95. It sat in the mid-90s for the rest of a 11-pitch inning on Saturday. He struck out three batters in an inning of work on Tuesday.
Jansen, who missed three weeks with an irregular heartbeat, will undergo an offseason catheter ablation. He said he expects to need three months to rehabilitate.