ST. PETERSBURG, Fla. --Ty Wigginton turned the game with his second tying homer and Brendan Harris finished the job with his first game-ending hit.
"I know our guys believe they get it done," Tampa Bay manager Joe Maddon said.
Ben Zobrist, who was in a 1-for-25 slump, had a one-out infield single off Jay Marshall (1-2) in the 12th. He went to second on a wild pitch and scored on Harris' two-out hit down the right-field line.
"It's great," Harris said. "If anybody else had got it, after 12 innings it's nice to end it with us on top."
Ruddy Lugo (2-0) worked out of two-on, two-out jam in the 12th for the win.
Wigginton's second homer tied the score in the ninth against Oakland closer Huston Street, who had converted eight of his previous nine save chances. It was the first home run allowed by Street in 52 games, dating back to last June 24.
"I'm not surprised because he's as nasty as they come," Wigginton said of Street's streak. "I was just trying to look for something up in the zone and I got a pitch up in the zone that I was able to get a hold of. Really, just trying to find a way on base."
Street hadn't allowed a run in 12 games, covering 12 2/3 innings, previously against the Devil Rays.
"Just one pitch, a slider up and Wigginton didn't miss it," Oakland manager Bob Geren said.
The blown save cost Joe Kennedy his first win of the season. He allowed three hits, two walks and struck out three in seven innings. The left-hander has given up just five earned runs over 28 innings in five starts.
"That's baseball," Kennedy said. "Wins come and wins go. You can't sit there and reflect on the fact that you didn't get a win. As long as you just keep going out and establishing a presence out there, the wins will come."
The Athletics went up 2-1 in the eighth on Bobby Crosby's two-out RBI single off Jae Kuk Ryu.
Tampa Bay's B.J. Upton, who entered as the AL batting leader, went 1-for-5 and had his average drop 10 points to .376.
Devil Rays starter Scott Kazmir allowed one run and five hits in six innings. He struck out eight and walked three during a 105-pitch outing.
"It felt like I was throwing it where I wanted to, I wanted to establish inside early," Kazmir said.
Nick Swisher put the Athletics up 1-0 with an RBI single in the third. He had a homer and drove in four runs in Oakland's 5-2 win over Tampa Bay on Friday night.
Wigginton's first homer of the game tied the score in the seventh.
The Devil Rays had just three batters reach base -- Upton's infield single in the second and a pair of walks by Delmon Young -- in the first six innings.
Young had walked just four times in his previous 29 games this season. Mired in a 1-for-22 slump, Young singled in the seventh.
Oakland, which went 2-for-14 with runners in scoring position Friday, were successful on just one of seven chances in the first three innings against Kazmir.
Kazmir was hit on the thigh by Crosby's grounder in the sixth, but recovered to throw out the Oakland shortstop at first. Kazmir said he fine after the game. ... Swisher, coming off a left hamstring injury, was the DH for the second straight game. Geren said Swisher might play in the field Tuesday. ... Wigginton has four career multihomer games. ... Oakland OF Milton Bradley (sore right wrist and strained left hamstring) had his appointment with a hand specialist moved back one day to Sunday. Geren said it looks less likely Bradley will be activated from the DL when eligible Tuesday because he hasn't taken BP left-handed.