Now, they head home for a four-game series against San Diego needing a victory or a loss by Milwaukee to get into the postseason.
"I don't think anyone's down in here," catcher Andrew Susac said despite the somber demeanor and quiet atmosphere. "We're just going to keep playing hard and good things will happen. We've got to take it to San Diego and get a little different outcome playing at home."
Tim Hudson (9-13) gave up three runs and five hits in 5 1/3 innings, struck out four and walked one for the Giants, whose only run came in the third when Hunter Pence scored on Joaquin Arias' fielder's choice to third base.
"It's tough when you're not getting runs on the board," Giants manager Bruce Bochy said. "We've got to get these bats going. We're going to see some good pitching (against San Diego) so hopefully we can get this figured out."
The Dodgers tacked on four more runs in the eighth, when Giants pitchers walked four batters and hit another.
The Dodgers claimed their second straight division title behind Kershaw (21-3), the probable NL Cy Young Award winner and MVP candidate who has been the catalyst behind their success this season.
He didn't pitch lights out — getting called for a balk and wild pitch — and he committed a throwing error in the seventh but he did a little bit of everything, including hitting and fielding to ensure the Dodgers' celebrated in front of their longtime rivals.
Kershaw allowed one run and eight hits in eight innings, struck out 11 and walked none in his last start of the regular season, having won his final seven starts. He became the first player to lead the major leagues in ERA (1.77) in four consecutive seasons.
Kershaw tied his career high in wins from 2011. The Dodgers are 23-4 in his 27 starts this season.
The Dodgers snapped a 1-1 tie in the sixth, with Puig hitting a leadoff homer off Hudson to get things started. Crawford's two-run double off Javier Lopez made it 4-1 and Uribe followed with a RBI single off Jean Machi for a 5-1 lead.
"I threw that 0-2 pitch to Puig and somehow he managed to stay on a fastball," Hudson said. "I might've thrown him one the whole night, and he hits it out to right field. From there, it just kind of unraveled."
Kershaw tied the game 1-1 with his first career triple in the fifth, scoring Crawford, who got hit in the left foot by a pitch and then stole second. Kershaw chugged into third base standing up.
Kershaw had a bit of a messy third, when he allowed four baserunners, his most of any inning. With runners on first and second he was called for a balk, allowing the runners to move up. Kershaw showed quick reflexes facing his next batter. Hudson hit a comebacker and Kershaw, down on his right knee with his back toward the plate, reached around, backhanded the ball and threw to first for the out.
The 16-year veteran reached the 3,000 innings plateau, becoming just the second active pitcher to go over the mark. Mark Buehrle is the other at 3,076 2/3 innings pitched. Hudson's 13 losses are a career high.
Giants: C Buster Posey started at first base. He experienced tightness in his back after catching all 13 innings on Monday and eight on Tuesday. ... OF Michael Morse (strained oblique) is questionable for the San Diego series starting Thursday.
Dodgers: LHP Hyun-Jin Ryu (shoulder inflammation) is expected to throw from a mound in the next day or so, but there are no plans for him to pitch before the playoffs begin.
Giants: Yusmeiro Petit (5-5, 3.63 ERA) starts the series opener at home against San Diego. The right-hander joined the rotation on Aug. 28 in place of Tim Lincecum. He is 1-1 with a 1.35 ERA in four appearances against the Padres.
Dodgers: Roberto Hernandez (8-11, 4.08) starts the series opener against Colorado. The right-hander last faced the Rockies on Sept. 15 on the road, allowing two runs and six hits in 3 2/3 innings, but didn't factor in the decision in an 11-3 victory.