TORONTO -- Jon Lester felt bad about letting down Boston's batters.
Even with that support, Lester wasn't able to keep the Blue Jays in check.
"I basically ruined a good night for the offense," he 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.
"It was uncharacteristic," Red Sox manager Terry Francona said. "He wasn't pumping strikes, he wasn't throwing it where he wanted to. It looked like he was a little bit frustrated."
Lester acknowledged losing his cool, and said it hurt him on the mound.
"I have to do a better job of controlling my emotions and not worrying about [calls] and worrying about the next pitch. I didn't do a very good job of that," he said.
"If we get the ball in the air on the one to second, we got him," 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.
Albers and Varitek shared the blame for allowing the speedy Davis to reach third base.
"I shouldn't have let him steal third," Albers said. "I think that one was on me. I've got to keep him closer and keep him at second."
Varitek said the throw to third was a tough one.
"[Davis] had a pretty good jump, and we had a breaking ball called," he said.
Carlos Villanueva (1-0) pitched a scoreless inning for the win.
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 Blue Jays shortstop Yunel Escobar, who left after he was hit just above the left ankle by a pitch from 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."
The Blue Jays had lost three straight and seven of nine coming in, but 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.
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.
Jacoby Ellsbury's first-inning single extended his hitting streak to 19 games, while Crawford's RBI single in the second extended his hitting streak to 10 games. ... Blue Jays 1B Adam Lind (sore back) missed his second straight start. Manager John Farrell said Lind is feeling better, and has not yet had an MRI or X-rays.