The victory before a Rogers Centre crowd of 21,698 tied the three-game series at 1 -- with the finale Sunday afternoon -- and put the Blue Jays' record at 9-4.
Tallet's effort nearly ended as soon as it started, when his second pitch was hit back at him by Ryan Sweeney and hit him on his pitching hand.
Tallet's hand was numb when he picked up the ball, and he threw wildly to first. The error put Sweeney at third base, and he scored on Jason Giambi's one-out grounder to second.
Tallet didn't allow another run until his final batter, Giambi, doubled home Sweeney, who also had doubled.
Shawn Camp, Scott Downs, B.J. Ryan, Jesse Carlson and Frasor all took their turns at holding the Athletics, while the Blue Jays were able to find the runs to put the game away.
Tallet said he doesn't consider himself a reliever or a starter, just a pitcher.
"To me, it doesn't matter as long as I'm pitching," Tallet said. "I've been getting a lot of jokes about being a new starter, No. 5. I always say I'm not a starter, I'm not a bullpen guy, I'm a pitcher. If I get to start, I start, if I get to relieve, I relieve."
Even though the game went on for a long time after Tallet's departure, manager Cito Gaston was appreciative.
"He gave us some room there to not use our bullpen so early, even though we did use it all," Gaston said. "But without him, it would have been worse. The bullpen did a really good job, they really did."
The bullpen's work set up Overbay's big hit against Dan Giese, who pitched 2 2/3 innings in taking the loss.
Giese walked Jose Bautista with two out and then served up Overbay's home run to right-center on a 1-0 pitch.
"I was just looking for something up in the zone that I could drive," Overbay said. "He's a guy who has to throw everything, and it was just a matter of getting a good pitch to hit."
"For us to get out of the game with a 'W' is huge," Tallet said. "Because now we get back to guys who have been starting in the rotation and have their pitches built up and can get us deeper into the games."
Tallet was able to get by on 67 pitches, 41 strikes, with a limit that was going to be about 70. Oakland starter Trevor Cahill needed 93 pitches to go 5 1/3 innings, as he allowed five hits, five walks and two runs.
The Blue Jays tied the game twice. In the fourth, they scored a run with the help of three walks from Cahill. Travis Snider's fielder's-choice grounder scored the run. The inning ended on a brilliant run-saving play by Orlando Cabrera on Aaron Hill's grounder to the hole at shortstop.
The Blue Jays tied it in the bottom of the sixth on Snider's one-out single to right. It scored Overbay, who opened the inning with a double and was sacrificed to third by Rod Barajas. Cahill was replaced by Michael Wuertz after Snider's single.
Toronto had a chance to win in the ninth thanks to former Athletic Marco Scutaro, who led off with a walk, daringly took second on Hill's fly out to deep center and stole third. Alex Rios walked but Vernon Wells and Adam Lind could not bring him home and the game went to extra innings.
It appeared that Tallet's afternoon might be short after Sweeney's shot hit him between the pinkie and ring finger.
"When I went to pick that ball up I had no feeling in my hand," Tallet said of his wild throw to first.
After a visit by trainer George Poulis and Gaston, Tallet took a few warmup pitches and continued.
"Until after that first warmup pitch, it was still a little numb," Tallet said. "When [the first warmup pitch] came up a little high they said, 'Hey, don't try to be a hero.' The next couple of pitches I got a decent feel of the ball and threw a little breaking ball in there to see if it would affect that, and it didn't. So I told them, 'I'm good.'"
On his first pitch after getting hit he got a groundout from Cabrera.
"I was able to keep it loose," Tallet said. "It was one of those things where as long as I was able to throw the ball I was going to take it."
It ended up being enough to keep the Jays in the game and eventually win it. But was it enough to earn another start?
"Absolutely," said Gaston.