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SAN FRANCISCO -- Clayton Kershaw pitched with a Giants fan on his mind.

This was far from a routine night in the longtime rivalry between San Francisco and Kershaw's Los Angeles Dodgers.

Kershaw shut down the Giants again with his big-breaking curveball, Rod Barajas homered and the Dodgers beat San Francisco 6-1 on Monday night when players from both teams denounced violence between their hard-core supporters.

Kershaw (2-1) struck out seven, walked two and gave up six hits in 6 2/3 innings, and he hasn't allowed a run over his last 23 2/3 innings against the Giants. That includes seven scoreless innings on Opening Day and a complete game last Sept. 14 at AT&T Park.

But the Dodgers lost shortstop Rafael Furcal to a broken left thumb that likely will land him on the disabled list Tuesday.

This game was dedicated to longtime Giants fan Bryan Stow, who was severely beaten by two men in Los Angeles gear outside Dodger Stadium after the teams' March 31 season opener. Stow, 42, is at a Los Angeles hospital in critical condition and in a medically induced coma.

"Tonight was an emotional night with the Stow family and everybody's thoughts (with them)," Kershaw said. "It was a special night with both teams having a common goal in mind. I thought the fans were awesome."

It's was a rare sight before first pitch: players from both teams coming to the mound together to address fans. Giants reliever Jeremy Affeldt and Dodgers second baseman Jamey Carroll took turns providing a joint message to the sellout crowd of 40,870: This rivalry must stay on the field, without violence and hatred.

"This game is not about violence, it's about having fun," Dodgers center fielder Matt Kemp said after the game.

The Giants heightened security at AT&T Park in the wake of what happened -- as is standard practice when the Dodgers come to town anyway.

"I thought the fans were awesome," Kershaw said.

Andre Ethier had a pair of run-scoring singles and Kemp also added an RBI single in the Dodgers' four-run fifth against Madison Bumgarner (0-2), started by Barajas' drive to left-center for his second homer of the year.

Pat Burrell broke up Los Angeles' shutout bid with a solo homer against Mike MacDougal leading off the ninth that hit the left-field foul pole.

After a jam-packed weekend of World Series celebrations, the Giants presented former infielder Juan Uribe with his championship ring before the game. Then, the tone became far more serious.

Carroll delivered his message then had three hits in the Dodgers' third win in four tries against the reigning champions. Carroll also had three hits Saturday at San Diego after producing four three-hit games all of last season.

Los Angeles' top three hitters went a combined 6 for 11 with a walk over the first seven innings.

The first seven batters reached base against Bumgarner in the fifth. Furcal was hurt after being called safe on a close play at third base by Todd Tichenor, a call-up umpire from the minor leagues. It was Furcal's first stolen base but the injury wasn't clear because he stayed in the game for two more defensive innings before Aaron Miles pinch-hit in the seventh. The Dodgers made two outs on the bases in the fifth.

"It was me not being able to put guys away, get them out," Bumgarner said of the fifth. "It was a frustrating game. A lot of things didn't go my way."

Aubrey Huff had two hits for the Giants, who were coming off their first series victory of 2011 against St. Louis over the weekend. San Francisco lost two of three to open the season at Dodger Stadium, both by one run. The Giants have been held to one or fewer runs in four of their six losses.

"We need a better game plan for him. He's tough, no doubt about it," Burrell said of Kershaw. "He's one of the tougher guys out there."

Bumgarner, the 21-year-old lefty who shut out the Texas Rangers in Game 4 of the World Series as a rookie, was tagged for five runs on eight hits in five innings.

Last season, he went 6-3 with a 1.91 ERA in 10 outings away from the Giants' waterfront ballpark last season and 1/3 with a 4.60 ERA in eight starts at home.

The Dodgers won five championships since coming to California in 1958 before the Giants got their first in San Francisco last fall.

The last time these two rivals met with the Giants as champion was so long ago that the game featured Hall of Famer Willie Mays homering off Carl Erskine at Ebbets Field in New York's 7-5 loss to the Brooklyn Dodgers on Sept. 18, 1955.

Los Angeles third baseman Casey Blake, who started the season on the disabled list with a back injury, was out of the lineup for the second straight game after a Saturday collision with San Diego baserunner Chase Headley. Blake has soreness in his upper left thigh that worsened over night into Monday.

Game notes

Kershaw lowered his ERA from 2.08 to 1.37. ... Kemp stole his seventh base for the Dodgers in the second inning after drawing a leadoff walk. ... The Giants plan to decide Tuesday whether injured CF Andres Torres, who strained his left Achilles' tendon Saturday night, will need a disabled list stint. They don't want to go short-handed for long. Miguel Tejada batted leadoff in Torres' usual spot Monday. ... Injured Giants RF Cody Ross has resumed jogging and outfield work as he recovers from a strained right calf that landed him on the DL to start the year. He gave a thumbs-up sign after the workout. Ross is slated to get some at-bats in extended spring training when the team heads to Arizona this weekend, then play in a couple of minor league games for a short rehab assignment. ... Bumgarner faced the Dodgers for the first time at home.