TORONTO - Speed is the new weapon for the Blue Jays, and no Toronto player has more of it than Rajai Davis.

Davis stole two bases in the 10th inning, setting himself up to score the winning run on David Cooper's sacrifice fly, and the Blue Jays beat the Boston Red Sox 7-6 on Tuesday night.

"(Davis) created that run," manager John Farrell said.

Cooper also hit his first major league homer as Toronto improved to 4-1 in extra innings.

Jose Bautista hit his 11th home run of the season and rookie J.P. Arencibia also went deep for the Blue Jays, who had lost three straight and seven of nine.

Carlos Villanueva (1-0) pitched a scoreless inning for the win.

Adrian Gonzalez homered twice for the Red Sox, the 11th multihomer game of his career, and David Ortiz added a solo shot.

Davis hit a one-out single off Matt Albers (0-1) in the 10th and stole second on the first pitch, a pitchout, sliding in just ahead of the tag on a low throw from catcher Jason Varitek.

"If we get the ball in the air on the one to second, we got him," Red Sox manager Terry Francona said.

Davis stole third on the very next pitch, and the Red Sox brought their infield in. Cooper won it with a fly to center.

"Once I saw (Davis) get those two bags I was like, just get something to the outfield and let's win this game," Cooper said.

Davis, who stole a career-high 50 bases for Oakland last season, sensed an opportunity when he reached base against Albers.

"I just felt that he was going to be pretty slow to the plate and he wasn't paying me much attention," Davis said. "So I was able to take advantage of the opportunity that he gave me."

The Blue Jays, who led the majors with 257 home runs last season, are second in the AL in steals with 38 this year, behind only Kansas City. In the NL, San Diego had 38 steals entering play Tuesday.

The Red Sox, who had their three-game winning streak snapped, were trying to reach the .500 mark for the first time this season.

"Whatever our record is, we always want to win these games," Francona said. "We want to win every game. That's how we always feel. I don't care what our record is."

Cooper entered in the sixth as a replacement for shortstop Yunel Escobar, who left after he was hit just above the left ankle by a pitch from Jon Lester. Escobar is day-to-day.

Toronto took a 6-5 lead when Cooper connected off Daniel Bard to begin the eighth, but Gonzalez answered by opening the ninth with a solo drive to left off Frank Francisco, who had his first blown save.

"We're seeing what everybody has talked about," Francona said of Gonzalez. "When he leverages the ball to left field, he looks like a right-handed hitter."

Toronto jumped on Lester with three in the first, taking advantage as the lefty walked three of his first four batters. Lester's third base on balls, to Edwin Encarnacion, came with the bases loaded. Aaron Hill and Juan Rivera followed with RBI grounders.

"We started out in a hole and that's a hard way to play," Francona said.

Lester, who failed to extend his winning streak to five starts, allowed five runs and seven hits in 5 1-3 innings. He matched a career high with five walks and struck out five.

"I basically ruined a good night for the offense," he said.

Boston got one back on Carl Crawford's RBI single in the second and cut it to one on a leadoff homer by Ortiz in the fourth, his fifth.

Gonzalez gave the Red Sox a 4-3 lead with a two-run shot to left in the fifth, his fifth, but Bautista tied it with a leadoff shot in the bottom half.

Arencibia restored Toronto's lead when he opened the sixth with a drive to left, his fifth.

The Red Sox tied it in the eighth against Toronto lefty Marc Rzepczynski. Jed Lowrie doubled and was replaced by pinch-runner Jose Iglesias, who went to third on Crawford's grounder. Jarrod Saltalamacchia tied it with a two-out single.

Toronto rookie Kyle Drabek allowed four runs and eight hits in five innings. He walked three and struck out five.