The Dodgers have won six of their past seven series at home heading into a day off Thursday before Colorado arrives for a weekend series.
Jamey Wright (2-2) pitched two perfect innings and struck out two for the victory.
Lincecum (2-3) gave up four runs and eight hits in five innings. He struck out eight, including NL home run leader Matt Kemp three times, and walked two in losing for the first time since April 16 against Philadelphia.
The right-hander extended his winless streak against the Dodgers to 0-4 dating to last season. The two-time NL Cy Young winner has been especially hard-hit in the first inning, but he got out of that having allowed just two hits.
Kemp, who came in batting .500 in his 11 previous home games against the Giants, went 0 for 5.
The Dodgers struck for four runs in the fourth to take a 4-2 lead. Lincecum gave up a leadoff double to Andre Ethier and Bobby Abreu followed with a single. Juan Uribe drove in Ethier with a single to third that Joaquin Arias, who fell down before he could get off the throw to first. A.J. Ellis walked one out later and Gwynn cleared the bases with a drive into deep right field while batting for Chad Billingsley.
Buster Posey's RBI single in the third extended the Giants' lead to 2-0. Brandon Belt reached on a fielder's choice grounder and Schierholtz singled him to second. Arias had a single to center, and Kemp charged the ball, throwing to second baseman Adam Kennedy for the tag on Schierholtz, who had rounded the bag and was tagged out before Belt could cross the plate.
Lincecum drove in the Giants' first run with a single to shortstop in the second.
Billingsley lasted just four innings for the Dodgers, allowing two runs and seven hits while striking out five and walking four.
Notes: Dodgers OF-1B Juan Rivera was placed on the 15-day disabled list on Wednesday with what the team called a significant strained left hamstring. Manager Don Mattingly said Rivera would be out longer than two weeks. OF-1B Scott Van Slyke was recalled from Triple-A Albuquerque and got his first major league hit with a RBI single in his first major league at-bat in the sixth. He is the son of former major leaguer Andy Van Slyke. ... Dodgers INF Jerry Hairston was set to have a MRI on his strained left hamstring after missing his third straight game. ... Giants OF Angel Pagan was held out of the starting lineup although he felt well enough to play. He had a cramp in his left hamstring while beating out an infield single Tuesday. Gregor Blanco replaced him.
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