The 35-year-old left-hander tossed two-hit ball over five innings, Mookie Betts hit a two-run double that set a record of 105 RBI for a leadoff hitters and the Dodgers beat the San Francisco Giants 7-0 on Saturday night.
The NL West champion Dodgers clinched a first-round bye in the postseason. They earned their 95th win and 15th shutout, tied for second in the major leagues behind Seattle's 16.
Kershaw (13-4) struck out five and walked two in winning his 210th game, breaking a tie with Don Drysdale for second on the Dodgers' career list behind Don Sutton's 233.
"I have a lot of respect for Don Drysdale and what he meant to this organization, so it's a huge honor to get to do that," Kershaw said. "Wins are just being on good teams and being in the right spot."
Kershaw will pitch on six days' rest again next Saturday, when the Dodgers are in San Francisco.
"I'm on the college schedule, I'm a Saturday starter," he joked. "We're doing everything for a reason around here so take the extra rest when you can get it."
The three-time Cy Young Award winner has not gone beyond five innings in any of last seven starts. He returned Aug. 10 after missing six weeks with a left shoulder injury that he and the team have said little about.
"At the end of the day, you just have to execute pitches," Kershaw said. "It's as simple as that regardless of what your velocity is or how your stuff is moving."
In seven starts since coming off the IL, Kershaw has a 2.03 ERA with 27 strikeouts and 14 walks.
Betts' RBI are the most by a leadoff hitter in a single season, two more than Charlie Blackmon's 103 for Colorado in 2017. Betts' double in the eighth extended the lead to 7-0.
"There's been a lot of great leadoff hitters and for him to be number one is pretty remarkable," Dodgers manager Dave Roberts said. "It seems like every night we're eclipsing milestones as individuals."
J.D. Martinez hit his 31st home run and added a two-run double after fouling a ball off near his ankle. The Dodgers could have three players with 100 RBI for the first time since moving to Los Angeles in 1958. Max Muncy has 103, and Martinez (98) and Freddie Freeman (96) are approaching triple digits with seven games remaining.
Freeman got his major league-leading 57th double of the season in the fifth, driving in Austin Barnes. Muncy's RBI single extended the lead to 5-0.
Freeman is three away from the first 60-double season since Charlie Gehringer and Joe Medwick in 1936.
He singled in the seventh for his career-high 203rd hit, then stole his 22nd base in 23 attempts.
The Giants had runners at the corners in the fifth after Marco Luciano's leadoff double and a walk to Luis Mato with two outs. David Peralta made a diving, inning-ending catch on Austin Slater's fly ball to left that potentially saved two runs. Kershaw looked up at his wife, Ellen, and children watching from a suite and smiled and waved as he reached the dugout.
"They're up past their bedtime. This time of year it's hard for them to be around, so it's always special to get to see them in the stands," Kershaw said, with his 6-year-old son, Charley, watching from the side of the room.
Giants opener John Brebbia (3-2) took the loss, pitching 1 1/3 innings.
San Francisco has lost seven of nine and been outscored 57-32 with one game remaining on its trip.
Giants: RHP Jakob Junis left after the fourth inning because of neck tightness. ... LHP Scott Alexander is on the 15-day IL with a left hamstring strain.
RHP Lance Lynn (12-11, 5.92 ERA) starts Sunday for the Dodgers.
AP MLB: https://apnews.com/hub/mlb