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TORONTO -- Jake Peavy is doing everything he can to get a win. Unfortunately, his teammates can't seem to score enough to make that happen.

David Cooper singled home the winning run in the 11th inning as the Toronto Blue Jays beat Chicago 3-2 on Monday night, handing the AL Central-leading White Sox their 16th loss in 19 games in Toronto.

Peavy allowed two runs and five hits in eight innings, lowering his ERA to 3.04. He walked two and struck out six.

But the All-Star right-hander lost for the eighth time in his past 11 starts, largely because he seldom gets enough offensive support.

"This is kind of the underlying theme with my season," Peavy said.

Chicago has scored just 26 runs in Peavy's past 11 starts.

"For one reason or another, we don't seem to score too much for him," manager Robin Ventura said. "He always goes out there knowing each pitch can cost him. We need to do a better job of giving him more room to pitch with."

Rajai Davis popped out to open the 11th before left-hander Leyson Septimo came on to replace Jesse Crain. After Septimo (0-2) walked Johnson on four pitches, Ventura brought in Nate Jones to face Edwin Encarnacion, whose single moved Johnson to third. Cooper followed with a liner that bounced just in front of a hard-charging Alex Rios in right, scoring Johnson easily.

"Tough night," Peavy said. "You want to win. We need a win coming down the stretch and at the start of a road trip like this."

The White Sox have lost four of six, but Detroit's loss at Minnesota kept Chicago's two-game lead atop the Central intact.

Chicago's Adam Dunn hit two home runs, including a game-tying shot in the ninth inning, boosting his major league-leading total to 33. It was his 32nd career multihomer game and second this season.

"Besides Adam, we didn't really get anything going, didn't look fluid or anything," Ventura said. "We have to get something else going besides waiting for home runs."

Dunn was at a loss to explain Peavy's hard luck, and the lack of runs in his favor.

"We just can't seem to score runs when he's on the mound," Dunn said. "He keeps us in every single ballgame."

Steve Delabar (3-1) struck out six batters in two innings to earn the win.

Delabar struck out four in the 10th, the first time a Blue Jays pitcher has accomplished the feat and the first time in major league history it has happened in extra innings. White Sox catcher Tyler Flowers, the second batter of the inning, struck out swinging but reached on a passed ball.

With Chicago trailing 2-1 to begin the ninth, Dunn tied it by swatting Casey Janssen's first pitch over the wall in left, giving him 1,000 career RBIs.

"We need more people swinging like he did tonight," Ventura said.

For Janssen, the blown save was his first since April 14 against Baltimore, snapping a streak of 15 successful conversions.

Dunn's first homer was a mammoth 469-foot shot off the roof of the restaurant in center field in the fourth.

"Dunn makes the park look like a Little League field every time up," Blue Jays manager John Farrell said.

The drive was the longest home run at Rogers Centre this season. Encarnacion hit a 467-foot homer against Cleveland on July 14.

Toronto opened the scoring in the third when Anthony Gose was hit by a pitch, moved to second on Johnson's two-out walk and scored when Encarnacion followed with a single to right.

Rookie Moises Sierra restored Toronto's lead when he opened the seventh with a homer to left-center off Peavy, the first of his career.

"It was a good pitch, changeup down and away," Flowers said. "Sometimes they guess right and I think that's what happened."

Toronto right-hander Carlos Villanueva allowed one run and five hits in a season-high seven innings. He walked one and matched his career-high with eight strikeouts.

Chicago's Kevin Youkilis returned to the lineup after sitting out Sunday's win over Oakland with soreness in his left arm and right knee.

Game notes

White Sox 1B Paul Konerko cleared a battery of post-concussion tests Monday and will resume physical activity Tuesday. ... Chicago recalled LHP Donnie Veal from Triple-A Charlotte. He replaces OF Jordan Danks, who was optioned to Triple-A Sunday. ... Toronto OF Jose Bautista (left wrist) swung the bat and hit off the tee before the game. For Bautista, it was his first activity since Aug. 1, when he was shut down with lingering pain. ... Flowers caught for Chicago, with A.J. Pierzynski starting at DH. ... Blue Jays RHP Brandon Morrow (strained muscle in his left side) will make two more minor league rehab starts before rejoining the team, Farrell said. Morrow has already made three rehab starts and will make his fourth on Tuesday at Double-A New Hampshire. ... The White Sox have hit 20 homers in their past 10 games.