Justin Sellers triggered a four-run seventh inning with his first home run of the season for the NL West-leading Dodgers, who improved the best record in the majors to 27-13.
Kershaw (4-1) got the seventh complete game of his career, striking out four and not allowing a runner past second base against an offense that came in leading the NL in team batting average, runs, homers, on-base percentage and slugging percentage. He did not walk a batter for the third time this season while lowering his ERA from 2.22 to 1.90.
Kershaw, the reigning NL Cy Young winner, is 14-1 with a 1.40 ERA in his last 19 starts at home.
The Dodgers beat the defending World Series champions for the sixth straight time - their longest winning streak against the Cardinals since an eight-game stretch from July 24, 1975 through May 12, 1976.
Westbrook (4-3) was charged with four runs - three earned - and six hits in 6 1-3 innings. The 34-year-old right-hander, pitching at Dodger Stadium for the first time in his 12-year career, departed after giving up Kershaw's opposite-field double off the glove of left fielder Matt Holliday. It was Kershaw's first extra-base hit after hitting 28 singles over five seasons.
Tony Gwynn Jr. greeted Eduardo Sanchez with a single that drove in Kershaw. The Dodgers got two more runs that inning when Gwynn scored on Sanchez's wild pitch and Andre Ethier added an RBI single that increased his NL-best RBI total to 36.
Matt Carpenter took over at first and committed a fielding error on a hard-hit grounder by former Cardinal Adam Kennedy in the fourth inning, allowing the game's first two runs to score. Kennedy, who had four hits in Friday night's series-opening 6-5 Dodgers victory, was credited with one RBI on the play.
The switch-hitting Berkman, a six-time All-Star and the NL comeback player of the year in 2011, has played in only 13 games this season and is batting .333 with a homer and four RBIs. He had just come off the disabled list last Sunday after being sidelined for 21 games because of a strained left calf he aggravated while chasing a popup.
In Friday night's series opener, he homered as a pinch-hitter against Dodgers closer Kenley Jansen with two out in the ninth to tie the score, before the Cardinals lost in the bottom half on a bases-loaded walk. The homer ended the longest season-opening home run drought of his career after 40 at-bats.
Dodgers catcher A.J. Ellis doubled his first two times up, and has reached base with a hit or a walk in 31 of his first 32 games - including the last 28 in a row. He entered Saturday with a .459 on-base percentage, the second-highest in the majors behind the Mets' David Wright (.510).
The Dodgers' injury jinx continued when second baseman Mark Ellis was placed on the 15-day disabled list Saturday because of a banged up left knee. He is the fifth position player and fourth regular that manager Don Mattingly has lost to the DL in a span of 11 days, including center fielder Matt Kemp, third baseman Juan Uribe, left fielder Juan Rivera and utility infielder Jerry Hairston Jr.
Ellis was injured during the seventh inning Friday night when he took a short toss from shortstop Dee Gordon on a fielder's choice grounder by Shane Robinson and was upended by Tyler Greene on a hard but clean straight-on takeout slide. Infielder Ivan DeJesus was recalled from Triple-A Albuquerque to fill Ellis' roster spot.
Notes: Gordon, the Dodgers' regular shortstop and leadoff batter, got the night off after going 2 for 31 with 10 strikeouts and one walk in the previous seven games. Mattingly said before the game that he will sit him for a few days. ... Kershaw, who led the NL with 248 strikeouts last season, has made 13 consecutive starts without reaching double digits in strikeouts. ... In eight starts this season, Westbrook has yielded just one run over the first three innings. He has made only two other regular-season appearances against the Dodgers, both in relief for Cleveland in 2003.
Link to boxscore: Los Angeles 6, St. Louis 0