OAKLAND, Calif. -- The Oakland Athletics were down to Josh Smith, their sixth and final available relief pitcher Sunday afternoon, when they came to the plate in the bottom of the 12th inning in a 5-5 game against the Minnesota Twins.

"Couple more innings and I wasn't sure what we were going to do," A's manager Bob Melvin said.

As it turned out, Melvin never had to face that problem, thanks to Yonder Alonso.

Alonso hit a solo walk-off home run with one out in the 12th, powering the A's to a 6-5 victory against the Twins at the Oakland Coliseum.

Alonso launched reliever Tyler Duffey's first pitch into the right field seats for his 22nd home run of the season. The walk-off blast was the second of his career.

The Athletics beat Minnesota with a walk-off homer for the second straight game. Rajai Davis hit a two-run shot in the ninth inning Saturday. Sunday was Oakland's ninth walk-off win of the season.

"It felt good," said Alonso, who has been in a hitting funk but went 3-for-6 Sunday. "For me, it was just coming back to the basics, making sure I was getting good pitches to hit, making sure I was using the whole field. I felt like I've been going out of my zone a little bit and trying to do too much."

A's starter Jharel Cotton lasted only 3 2/3 innings, but after he exited, Simon Castro, Liam Hendriks, Santiago Casilla, Blake Treinen, Ryan Dull and Smith combined to blank the Twins for the final 8 1/3 innings. Smith (1-0) pitched two shutout innings for the win. Duffey (0-3) took the loss.

"Everybody put up zeroes and it's definitely contagious," Smith said. "You want to come in and challenge hitters and throw a lot of strikes."

The Twins lost the series 2-1 and fell five games behind Kansas City in the race for the second wild-card berth in the American League.

"Anytime you get walked off, that's a tough way to lose a ballgame," Twins manager Paul Molitor said. "Today's game kind of mirrored some of the other ones on this trip. We did a fairly decent job early in the game pitching and putting some runs on the board but we got a little stagnant offensive. What we've been doing too much of is letting these teams hang around. We had a chance to increase our lead and (did) not take advantage."

In the first inning, Eduardo Escobar hit a two-run homer and Brian Dozier a solo shot for the Twins, who grabbed a 3-0 lead and extended it 5-0 through the top of the fourth. The A's scored twice in the fourth, once in the fifth and twice in the eighth to pull even.

Oakland rookie Jaycob Brugman hit a solo home run in the fifth, and rookie Matt Chapman had a two-run double in the eighth.

With two outs in the eighth, Ryon Healy worked a walk off Taylor Rogers and moved to second when pinch hitter Rajai Davis lined a single to center.

Chapman lined a two-run double to left off Ryan Pressly.

"I knew coming into that at-bat that the guy I was facing had some good stuff, had a live fastball and some good off-speed pitches," Chapman said. "I really tried to just bear down and stay short. My approach was I kind of choked up on the bat and I was not trying to do too much."

Cotton was activated Sunday from the disabled list and gave up five runs on five hits, including the two home runs in the first. He struck out five, walked five and threw 78 pitches. He had been out since July 4 because of a blister on his right thumb.

"Bullpen came in and did a great, great job," Cotton said. "They picked me up big-time on an afternoon when I didn't do my job."

Twins right-hander Bartolo Colon, who pitched for the A's in 2013 and 2014, allowed three runs on eight hits over 6 1/3 innings. He struck out one and walked one. Colon is 0-1 with two no-decisions for Minnesota since being called up from Triple-A Rochester on July 18.

"I feel good," Colon said. "I feel like this is one of my second homes. I thought it went well. I can't remember the last time I went past the sixth."

NOTES: The Twins traded LHP Jaime Garcia, along with cash considerations, to the New York Yankees on Sunday morning for RHP Zack Littell and LHP Dietrich Enns, a pair of minor league prospects. ... Twins DH Miguel Sano was ejected by plate umpire Phil Cuzzi in the 11th after taking a called third strike on a pitch that appeared to be outside, then slamming his bat down in anger. ... A's RHP Frankie Montas was optioned to Triple-A Nashville on Sunday, opening a spot on the 25-man roster for RHP Jharel Cotton. Montas is 1-1 with a 7.03 ERA in 23 relief appearances for the A's over two stints. ... A's INF/OF Chad Pinder (strained left hamstring) played his final rehab game for Triple-A Nashville on Saturday and will be activated Monday when the A's open their series against the Giants. ... 1B Joe Mauer played his 1,676th career game, tying him with Tony Oliva for fourth-place on the Twins' all-time list. ... Twins RHP Trevor Hildenberger, a product of the University of California in nearby Berkeley, had five strikeouts in two shutout innings of relief.