TORONTO -- In a battle of bullpens, the Oakland Athletics' relievers broke first.
Five Toronto relievers combined to work 6 2/3 scoreless innings, giving up only a single, and the Blue Jays beat Oakland for the seventh time in eight games.
Oakland's relief corps was almost as good, allowing only two hits, including Overbay's homer, in 6 1/3 innings.
"Both bullpens did a great job, they just got the big hit," Oakland manager Bob Geren said. "We only had five [hits] for the day. Five in 12 innings is not going to win too many games."
After a two-out walk to Jose Bautista, Overbay smacked a 1-0 fastball to center off Giese (0-1), who was called up from Triple-A earlier in the day.
"I was just looking for something up in the zone that I could drive," Overbay said.
"Obviously you'd like to get off to a little better start than I did today," Giese said. "It was just one bad pitch I left up. No excuses, it's just a bad pitch."
Right-hander Jason Frasor (2-0) got two outs to earn the win for Toronto.
In truth, Toronto's relievers handled the entire game, with left-hander Brian Tallet coming out of the bullpen to start in place of injured righty Jesse Litsch (right forearm). Making his first start since 2006, Tallet gave up two runs -- one earned -- and four hits in 5 1/3 innings. He walked one and struck out one.
"He gave us some room to not use our bullpen so early, even though we did use it all," Blue Jays manager Cito Gaston said. "Without him, it would have been worse."
The Blue Jays put the winning run at third base with one out in the ninth but couldn't convert against right-hander Santiago Casilla. Marco Scutaro led off with a walk, moved to second on Aaron Hill's fly to center and stole third on the first pitch to Alex Rios, who walked.
But Scutaro was caught in a rundown on Wells' grounder to second and Adam Lind struck out looking to send it to extra innings.
Tallet's start almost came to an early end when Athletics leadoff hitter Ryan Sweeney lined a single off the back of Tallet's hand in the first. Sweeney went to third on Tallet's throwing error and scored one out later on Jason Giambi's RBI grounder.
Toronto tied it in the fourth against right-hander Trevor Cahill, who walked the bases loaded before giving up an RBI fielder's choice to Travis Snider. Cahill reloaded the bases by hitting Scutaro but got out of it when shortstop Orlando Cabrera made a strong throw from the hole to get Hill at first.
"He's made some highlight-type plays already, three or four of them in this short season," Geren said of Cabrera. "It's a pleasure to watch him out there everyday, that's for sure. You can see why he has a couple of Gold Gloves."
Oakland went ahead in the sixth when Sweeney led off with a double, went to third on Cabrera's fly and scored on Giambi's double. Tallet left after Giambi advanced on a wild pitch.
Toronto answered in the bottom half. Overbay doubled, went to third on a sacrifice and scored when Snider singled through the drawn-in infield, chasing Cahill.
Cahill allowed two runs and five hits in 5 1/3 innings. He walked five and struck out one.
"He had one bad inning but, other than that, he was fantastic," Geren said. "Early on he was throwing nasty sinkers. You really don't know what it is, it's moving so much. I liked seeing that."
Rios snapped an 0-for-15 streak with a single in the third. ... Oakland's Nomar Garciaparra was held out of the lineup with a tight right calf, the same injury that forced him out of Tuesday's win over Boston. Garciaparra did not play Wednesday. ... Geren said 3B Eric Chavez (right shoulder) could play Sunday if he is able to hit and throw without pain before the game. ... Toronto placed C Michael Barrett (right shoulder) on the 15-day DL and purchased the contract of C Raul Chavez from Triple-A.