Brendan Ryan added a two-run base hit later in the sixth, helping the Mariners halt a six-game skid. Casper Wells and Jesus Montero both hit a solo homer in the first inning.
Hisashi Iwakuma (1-0) tossed two scoreless innings of relief to secure the win. Starter Kevin Millwood, who was coming off a no-decision in a combined no-hitter, was charged with four runs -- three earned -- over five frames.
Jeremy Affeldt gave up Gutierrez's go-ahead hit, but Tim Lincecum (2-8) was charged with the run and has now lost a career-high six straight games.
Ryan Theriot went 3-for-5 with two RBI for the Giants, who had won 10 of 14 coming in, including the opener of this three-game series on Friday.
In all, Lincecum gave up five runs on five hits. He walked two, struck out six and was relieved by Affeldt after allowing a leadoff single to Montero in the sixth. Hits by Michael Saunders and Dustin Ackley loaded the bases before Gutierrez slapped a grounder towards third. Joaquin Arias backhanded the ball, but his throw to first was late and Montero crossed the plate for a 5-4 lead.
"He was throwing well," Giants manager Bruce Bochy said of Lincecum's outing. "Looked like a good night for him after the first inning. I know he's taking it hard, he was pitching his heart out...it's hard to explain because he is so good at times. Then he has his hiccup innings and has a tough time staying out of the big inning."
Ryan's subsequent single up the middle capped the scoring.
The Giants have now lost each of Lincecum's last nine starts, although they did battle back to take the lead after Wells and Montero got to the two-time NL Cy Young winner early.
They manufactured a pair of runs in the third inning, which began with a Brandon Crawford double. Gregor Blanco then reached on an error by first baseman Justin Smoak and Theriot scored Crawford with a line drive to right. After a double-steal, Buster Posey tied the game with an infield single.
San Francisco took a 4-2 lead an inning later on consecutive two-out RBI singles from Theriot and Melky Cabrera. The base hits plated Brandon Belt and Crawford, who reached with a walk and a single, respectively.
Lincecum began to unravel in the fifth, allowing a leadoff single to Ackley before issuing a four-pitch walk to John Jaso. A sacrifice bunt advanced the runners and Ichiro Suzuki delivered and RBI single before Jaso scored the tying run on a wild pitch.
"He's a great pitcher (Lincecum) and it's easy to see why," Mariners manager Eric Wedge said. "I thought we did a good job of squaring up some fastballs and laying off some tough changeups as well, which I think made a difference for us."
The Giants are now 2-12 in games that Lincecum has started this season...Millwood had not pitched since leaving after six hitless innings against the Dodgers on June 8. Five Mariners relievers combined to work a final three hitless innings in that one.Seattle has homered in nine straight games, its longest streak since an 11-gamr stretch in 2009.
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