ANAHEIM, Calif. (AP) -- In a matchup of teams with hitting issues, a game of missed opportunities finally ended with a walk.
Anderson was the only batter he faced after replacing Freddy Dolsi (0-1).
"That was a walk-off win, and we'll take it," Los Angeles manager Mike Scioscia said with a smile. "We've been having trouble scoring the past 15-20 games, and our pitching has kept us in games."
The AL West-leading Angels won for the sixth time in their last eight, and Torii Hunter grinned and said, "We are struggling, but hey, we get a win. Our pitching and defense are getting it done. I'm getting gray hairs. And I don't have any hair."
The Angels and Tigers each went 0-for-12 with runners in scoring position.
Detroit and its high-priced lineup was shut out for a major league-high eighth time this season. The inconsistent Tigers had scored a total of 54 runs over a five-game stretch before they lost 1-0 to Minnesota on Sunday.
Maicer Izturis led off the 12th with a single, and, after Gary Matthews Jr. flied out, Vladimir Guerrero singled to center to advance Izturis to third. Dolsi (0-1) intentionally walked Hunter before Seay came on.
Seay said a checked-swing call that didn't go his way on his second pitch to Anderson was critical.
"The 1-0 pitch changed the whole at-bat," the Tigers' reliever said. "When you go back and look at the replay, he definitely swung at the ball on the second pitch.
"So the difference between 2-0 and 1-1 is a big difference. In a game like that, it's kind of unfair because we played that long. Coming in the bases loaded is a tough situation."
Jose Arredondo (1-0), the fourth Los Angeles pitcher, retired all six batters he faced in the 11th and 12th innings to earn his first major league win.
"I'm very excited," Arredondo said through a translator. "I'm just pleased to be up here."
Garland, who has been a Detroit nemesis in recent years, held the Tigers to four hits, walked two and struck out five before Scot Shields replaced him with one out in the eighth. Garland, formerly with the Chicago White Sox, came in with an 8-2 record in 12 starts against Detroit since Aug. 24, 2004.
Rogers scattered five hits, walked one and struck out two.
"Kenny Rogers was awesome tonight," Seay said. "He's a great pitcher. I think he'll definitely take positives out of it. He's been around the game a long time and I think he's starting to find his form again."
Detroit manager Jim Leyland was similarly impressed.
"You can't pitch any better than he pitched. He was much more aggressive. I thought he had good location, his ball sunk good and he kept the ball on the ground," Leyland said.
It was the Angels' first extra-inning game of the season. Los Angeles was the only team in the majors that hadn't played an extra-inning contest this year. It finally happened in the 53rd game, the longest such streak in club history from the start of a season.
Detroit DH Gary Sheffield left the game after feeling a muscle spasm in his left side when he grounded out in the third inning. "He's going to be evaluated further," Leyland said. "I would doubt that he'd play tomorrow. But how serious it is, I'm not sure yet." Ryan Raburn came on in the sixth to pinch-hit for Sheffield and remained in the game as the DH. ... The Angels recalled RHP Dustin Moseley, on the DL since May 2 with tightness in his right forearm, from rehab and assigned him to Triple-A Salt Lake.