It was Oakland's seventh win in eight meetings with the Blue Jays this season and pulled the A's into a tie with Boston in the AL wild-card race. The Red Sox lost to Texas 9-2 earlier Saturday. Oakland remains 6 1/2 games behind the Rangers in the AL West.
After losing to Toronto 11-0 Friday and finding themselves down again early, Jaha's game-tying homer was just the lift Oakland needed.
"That was great. That's what we were waiting for," said Olivares. "After that, everybody started being aggressive. The offense started right there and we kind of took off after that. The best thing I did was I just forgot about the first inning, put some zeroes on the board, gave us a chance to come back and win."
The A's improved to 6-3 in their 11-game stretch against Boston and Toronto, their primary competition for the wild card.
"We know where we are and it's great," Olivares said. "But the season is not over. We've got to come back out tomorrow and keep it going."
Added Jaha: "We're not worried about Boston or Toronto. We're just worried about ourselves nd winning more games. If we keep playing like we're playing, we're going to be there at the end."
Toronto, losing for the eighth time in nine games, was hurt by two bases-loaded walks issued by reliever Paul Spoljaric in the fourth inning and a pair of walks by starter Chris Carpenter before Jaha homered.
"We walked too many people tonight and that's how they won the game," Toronto manager Jim Fregosi said. "We didn't move our runners well. We had plenty of opportunities. We just couldn't move them tonight."
Olivares (11-9), acquired with Randy Velarde from Anaheim on July 29, trailed 3-0 before retiring a batter in the first inning but was tough on the Blue Jays the rest of the way.
He allowed four runs on seven hits in 6 1-3 innings to beat Toronto for the first time in six career decisions. He struck out two and walked three for his third win in five starts for Oakland.
Carpenter (9-7) couldn't hold a 3-0 lead, lasting three innings. He gave up six runs on seven hits while walking four and striking out three.
"I haven't done it for the last two starts," said Carpenter, who had a career-high nine walks in his previous start. "I had three runs and I didn't get it done. I haven't made any adjustments and we haven't figured out what I am doing wrong."
The Blue Jays began the game as if they were about to repeat their 11-0 drubbing of Oakland on Friday night. Shannon Stewart and Brian McRae hit successive singles to start the game, Shawn Green followed with an RBI double and Carlos Delgado hit a two-run single.
Jaha got the A's back in the game, connecting for his 28th homer in the third inning after Rich Becker and Jason Giambi walked. Matt Stairs and Ben Grieve hit consecutive doubles to put Oakland up 4-3.
Oakland loaded the bases in the fourth as Mike Macfarlane singled, Becker doubled and Velade walked. Spoljaric relieved and, sandwiched around strikeouts of Giambi and Stairs, he walked Jaha and Grieve to force home two more runs.
Macfarlane added a run-scoring double in the fifth and a final run on consecutive errors by first baseman Delgado in the eighth.
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