The AL East-leading Yankees, winless in eight games against second-place Boston, return home to open a four-game series against the Red Sox on Thursday night.
"We have to beat them at some point," Alex Rodriguez said. "This weekend is a good time to start."
Boston, the American League wild-card leaders, lost 6-4 at Tampa Bay on Wednesday.
"We're up 2 1/2 games on them," Damon said. "That's pretty good when you're 0-8 against that team during the season."
The Yankees, who last played Boston June 9-11, have been outscored 55-31 and are weary of talking about the poor record against their longtime rivals.
"You want to get that zero, that goose egg out of there," manager Joe Girardi said before the game. "We're going to be asked about that goose egg as long as it's there, so you want to get that out of the way as soon as possible."
Reliever Alfredo Aceves (7-1) pitched two innings for the victory as the Yankees used a four-run seventh inning to win their third straight overall after losing three in a row in Chicago.
"It was good to see him throwing the ball again like he's capable of doing, mixing all of his pitches and real crisp," Girardi said of Aceves.
Damon went 3 for 5 and hit his second homer in two games, a solo shot off Brian Tallet in the ninth, his 19th.
"He's really hit us hard this year," Toronto manager Cito Gaston said. "It's mostly been off-speed stuff. I think we'd better come up with something else to throw him."
The loser was Toronto left-hander Marc Rzepczynski (1-3), who allowed four runs and five hits in six-plus innings. He walked one and struck out seven.
New York sent 10 men to the plate in the seventh and erased a 3-2 deficit.
Melky Cabrera grounded out, moving Cano to third, and pinch-hitter Hideki Matsui hit an RBI single. Jose Molina walked and Derek Jeter struck out before Damon and Teixeira followed with run-scoring singles. Rodriguez walked to load the bases for Swisher, who struck out swinging on a 3-2 pitch.
Toronto took a 2-0 lead in the first against New York starter Sergio Mitre. The righty struck out the first two batters but followed that by giving up four straight hits, including RBI singles to Vernon Wells and Alex Rios.
The Yankees tied it in the third when Jerry Hairston walked, went to second on Jeter's single and scored on a base hit by Damon. Teixeira followed with an RBI fielder's choice.
Toronto chased Mitre in the fifth when Lind hit a one-out solo shot to right, his 23rd, and Lyle Overbay followed with a single to center.
Mitre, who allowed five runs and seven hits in just three innings in his last start, a 10-5 loss to the White Sox on July 31, was ineffective again in this one. The righty allowed three runs and eight hits in 4 1/3 innings and has not pitched into the seventh in any of his four Yankees starts. He walked two and struck out three.
"They made him work hard and I think he got a little tired at the end there but I think he threw the ball pretty well," Girardi said.
Scutaro led off the seventh with a homer to left off Aceves, his ninth, cutting it to 6-4.
Rodriguez started at DH but took over at third base in the seventh, forcing the pitcher into the lineup. Eric Hinske pinch hit for Coke in the seventh and restored New York's three-run cushion with a sacrifice fly off Jesse Carlson.
The Yankees recalled RHP Anthony Claggett from Triple-A Scranton/Wilkes-Barre and designated infielder Cody Ransom for assignment. ... RHP Joba Chamberlain, who will start against Boston Thursday, flew back to New York ahead of the team earlier in the day.