Lamonte Wade Jr. gave the Giants a 5-4 lead in the top of the inning with an RBI single, and Camilo Doval (0-2) struck out two batters with runners on second and third in the bottom of the inning.
Maton, though, hit a 3-0 pitch into the right-field stands for his first career game-ending home run.
“I knew I was going to get a fastball - something good to hit - and I was waiting for it,” he said.
José Cisnero (1-0) worked an inning for the victory.
Javier Baez, who was pulled from Detroit's 3-1 win in Toronto for a pair of baserunning mistakes and entered the game hitting .122, singled, doubled and walked twice.
Thairo Estrada reached base four times for the Giants, including a homer and a double.
The Tigers led 4-1 in the eighth, but J.D. Davis tied it with a three-run homer.
“The range of emotion in that game covered them all," Tigers manager A.J. Hinch said. “We knew we had an opportunity in the 11th inning if we could just get to our lefties. (Doval) is a really good closer, but when Maton gets into a hitters count, you aren't taking the bat away from him.”
Estrada started the game with his first career leadoff homer. The Tigers tied it in the second. Baez singled, took third on Eric Haase's double and scored on Spencer Torkelson's sacrifice fly.
Riley Greene's two-out triple scored Matt Vierling to put the Tigers up 2-1 in the third, and Baez made it 4-1 with a two-run double off Jakob Junis in the fifth.
The fifth could have been even bigger for Detroit, but third baseman Davis made a spectacular over-the-shoulder catch of Nick Maton's flare into shallow left.
“J.D. had a great game both with the bat and the glove,” Giants manager Gabe Kapler said. “That was a great play, plus the home run.”
The Giants went 1 for 10 with runners on base in the first seven innings, but Estrada led off the eight with a single, took second on a wild pitch and took third on Mike Yastrzemski's one-out single off Garrett Hill. Tigers manager A.J. Hinch brought in rookie Mason Englert, and Davis hit his first pitch into the right-field stands.
Giants: OF Austin Slater (hamstring) was scheduled to begin a rehab assignment with Triple-A Sacramento on Friday evening. ... OF Joc Pederson (wrist) went to the on-deck circle twice, but returned to the dugout both times. Kapler said he was trying to avoid an intentional walk since the Tigers didn't know Pederson couldn't swing. He said Pederson could be placed on the injured list if he can't play this weekend.
Tigers: OF Austin Meadows (anxiety) worked out with the team on Friday, but Hinch says there is no timeline set for his return to the active roster.
Doval might have gotten out of the 11th with the victory, but David Villar put him into a hole with a defensive mistake. Zach McKinstry led off the inning with a hard grounder to second and Villar threw to third to try to retire pinch-runner Ryan Kreidler. Kriedler was safe, meaning Doval's strikeouts of Jake Rogers and Matt Vierling weren't enough to end the inning.
“He thought the ball was taking him toward third base so he had a chance to make the play,” Kapler said. “But that's a play you rarely see made - it isn't even one we practice. You have to take the out at first.”
The teams play the second of the three-game series Saturday, with San Francisco's Anthony DeScalfani (1-0, 0.73) facing a yet-to-be-announced Tigers starter.
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