Carlos Frias, Adam Liberatore, Yumi Garcia and Chris Hatcher held the defending World Series champions two one hit over the final four innings, and Giants relievers George Kontos and Yusmeiro Petit gave up home runs to Joc Pederson and pinch-hitter Justin Turner in an 8-3 loss Monday night.
Dodgers lefty Brett Anderson failed to go the required five innings for a win. Frias (1-0) relieved him with two outs in the fifth and was credited with his second major league victory after pitching 1 1-3 innings and retiring Justin Maxwell on a comebacker with the bases loaded to end the Giants' three-run rally.
"Their 'pen shut us down, and that was the difference," Giants manager Bruce Bochy said. "They've always had some pretty good arms down there. They're missing their closer (Kenley Jansen), but they've got some power-type arms that have come out through their system. I thought our guys put up some pretty good at-bats against them in our series up in San Francisco, but tonight they pitched well."
Lincecum (1-2) gave up four runs, eight hits and three walks over four innings before he was lifted for a pinch hitter. The two-time NL Cy Young Award winner's fourth start of the season was delayed a day because of Sunday's rainout in Colorado.
"It didn't affect me," Lincecum said. "You've just got to lock in again. You know that day is over and you've got to move on to the next opponent. You go and study them, just like you would any other game. So it wasn't a factor."
Los Angeles snapped a scoreless tie with four runs in the third.
Howie Kendrick had an RBI single, then stole second, and Adrian Gonzalez scored when the throw from catcher Andrew Susac went into center field for an error. Scott Van Slyke singled as a pinch hitter for Carl Crawford, who left because of tightness in his right side, and Los Angeles capped the rally with Juan Uribe's RBI single and Pederson's run-scoring double.
"I was missing over the middle of the plate too much. And regardless of the ball being down or up, I'm missing on the sides of the plate that I shouldn't be missing on," Lincecum said. "Walks are going to kill you in situations like that. I started off the inning with a walk, and it just kept getting worse. It always comes down to the leadoff batter and getting him out. That changes the whole inning."
Anderson retired his first two batters in the fifth before giving up a walk to No. 8 hitter Brandon Crawford, a single by pinch-hitter Hector Sanchez, an RBI single by Nori Aoki and a run-scoring double by Joe Panik on Anderson's 74th and final pitch.
Angel Pagan greeted Frias with a run-scoring infield hit that was smothered by second baseman Kendrick, preventing Panik from scoring the tying run. Frias then retired Maxwell to preserve a one-run lead.
The game got off to an auspicious start on defense for the Dodgers. Aoki was off and running on Pagan's drive to the warning track in center field and was already past second base when Pederson made an over-the-shoulder catch and easily doubled Aoki off first with the help of shortstop Jimmy Rollins' relay throw.
"That was a Gold Glove-caliber play, to catch the ball and then fire a strike to the relay man to get Aoki at first," Anderson said. "He's made a couple of those plays behind me already, and also threw a guy out at the plate. He's been tremendous."
Giants: OF Hunter Pence, sidelined since spring training because of a broken left forearm, might be taking batting practice by next week.
Dodgers: RHP Brandon McCarthy, who signed a $48 million, four-year contract in December, will miss the rest of the season after an MRI revealed a torn ligament in his elbow.
Giants: LHP Madison Bumgarner (1-1) is 11-5 with a 2.58 ERA in 17 career starts against the rival Dodgers.
Dodgers: LHP Clayton Kershaw (1-1) will have a rematch with Bumgarner five nights after they hooked up in San Francisco. The 2014 NL MVP and three-time Cy Young Award winner is 1-2 with a 1.95 ERA in four starts against the big lefty. Bumgarner is 2-1 with a 3.20 ERA in his matchups against Kershaw.