The reward: A trip to the National League playoffs.
Center fielder Enrique Hernandez, left fielder Justin Ruggiano and catcher A.J. Ellis hit solo home runs off Bumgarner, the Giants ace, powering the Dodgers to the 14th NL West crown in franchise history.
"It feels really good," Dodgers manager Don Mattingly gushed after a champagne-and-beer shower. "This is a total organizational thing."
The Dodgers (88-69) will open the playoffs next Friday against the New York Mets (89-68), champions of the NL East. Home-field advantage in the best-of-5 series will be determined by best record at week's end.
LA will be making its third consecutive trip to the postseason, a franchise first. The Dodgers have earned a playoff berth in six of the last 10 seasons.
"Honestly, I did not want to lose this game tonight," Mattingly said of the prospect of seeing his team's lead potentially dwindle to four games with still two games remaining in San Francisco. "I didn't want this to drag on. I have too much respect for those guys over there (in the Giants clubhouse)."
The loss formally ended the Giants' bid for consecutive World Series championships. The club has won titles in 2010, '12 and '14, and then failed to make the playoffs the following season each time.
"We've been dealt with a tough hand with all the injuries," Bumgarner observed. "And here we are on Sept. 29. I think we should be proud of that."
In pitching the Dodgers to their first win in San Francisco in eight tries this season, Kershaw (16-7) got the better of Bumgarner (18-9) for the first time in four head-to-heads this season.
"I'm sure those guys are fine," Kershaw said of the Giants. "We might have clinched the division, but they've won three championships. They're still in a better spot than we are.
"We're trying to get to where they are."
Kershaw struck out 13, the 42nd double-digit strikeout outing of his career, and threw 104 pitches in running his career record against the Giants to 16-7.
The 13 strikeouts put Kershaw at 294 for the season. He's never recorded a 300-strikeout season.
"I was getting the first guy out every inning," he noted. "That keeps the pitch count down."
Hernandez homered in the third inning, and Ruggiano and Ellis went back-to-back in the sixth, running the Dodgers' season total to 184, which leads the league.
The Dodgers busted the game open in the eighth, using five consecutive hits, including a two-run, pinch-hit triple from Andre Ethier, to tack on four runs against the Giants bullpen and stretch their lead to 8-0.
"We really wanted to make Bumgarner work tonight," Mattingly said. "The early run (in the first inning) was big. Then the home run (by Hernandez). And Clayton was throwing zeroes."
Bumgarner was pulled with two outs in the sixth inning after Ellis' homer, trailing 4-0.
He failed for a third consecutive time to record a 19th win, allowing three earned runs on five hits. He walked one and struck out six.
The reigning World Series MVP had recorded 2-1 and 4-0 wins over Kershaw earlier in the season.
"It's not a good feeling," Bumgarner said of the Dodgers' on-field celebration. "You don't want to be a part of that. You want to be the one celebrating."
Hernandez, Ellis and first baseman Adrian Gonzalez had two hits apiece for the Dodgers, who had lost four in a row and eight of their last 10.
The Giants (82-75) had won three in a row, including 3-2 in 12 innings in the series opener Monday to keep their slim division hopes alive.
"Four concussions, three obliques and here we are," Giants manager Bruce Bochy praised. "When you go into the last week of baseball with a chance, and I told these guys, you have to be proud."
In just his second game back after a strained hamstring landed him on the disabled list, Hernandez got the Dodgers offense rolling immediately, leading off the game with a single.
He went to third when Giants second baseman Kelby Tomlinson booted a potential double-play grounder off the bat of Dodgers second baseman Howie Kendrick, and scored on third baseman Justin Turner's sacrifice fly.
The run was unearned.
As it turned out, that was all Kershaw needed en route to his third shutout of the season and fourth complete game.
NOTES: Dodgers manager Don Mattingly said he would talk to LHP Clayton Kershaw about the possibility of skipping his next scheduled start -- Sunday against the San Diego Padres -- to rest up for the postseason. "I know he'll want to pitch," Mattingly noted. ... Kershaw recorded the longest at-bat of his career in the fifth inning, a 13-pitch duel with Giants LHP Madison Bumgarner. ... Dodgers CF Enrique Hernandez's home run off Bumgarner in the third inning was measured to be 430 feet, the longest allowed by the Giants ace this season. ... Bumgarner allowed three home runs in a game for the fourth time in his career and second time at AT&T Park. ... Giants RHP Tim Lincecum (hip surgery) watched the game from the dugout for the final time this season. The pending free agent begins a rehab program in Arizona on Wednesday and hopes to be fully healthy by the start of spring training.