Derek Jeter added a two-run double and Cano continued his typical second-half tear with two RBI singles, his fifth straight multihit game as New York improved to 5-0 since the break.
"We're playing great right now," Cano said. "We're doing our job with men on base better than the first half."
New York's effective bullpen came through again after Darrell Rasner was pulled in the sixth, and the Yankees (55-45) reached 10 games over .500 for the first time this year. They moved within 3½ games of first-place Tampa Bay in the AL East, the closest they've been to first since play concluded on May 14.
The home winning streak is New York's longest since a nine-game run in May 2005.
"You've got to take advantage of being at home," manager Joe Girardi said. "The most important thing to me is that we're playing better."
Minnesota, which is 1½ games behind first-place Chicago in the AL Central, dropped to 3-18 at Yankee Stadium since the start of the 2002 season. The Twins (55-45) have lost seven straight series in the Bronx.
"We missed a couple plays out there, which always kills you in this ballpark," manager Ron Gardenhire said.
Trailing 2-1 in the sixth, New York got a rally going against Kevin Slowey (6-7), who was pitching for the first time in 12 days.
"I felt like it's not a good effort. It's my job to finish that sixth inning," Slowey said. "I made one mistake to Abreu and he kind of jumped on it. All it takes is one mistake."
The Yankees broke it open with four runs in the seventh.
Light-hitting rookie Brett Gardner drew a leadoff walk from Jesse Crain, and Damon reached on an error by third baseman Brian Buscher. Jeter grounded a two-run double down the third-base line and Abreu followed with an RBI double.
Giambi's run-scoring single off Brian Bass made it 8-2.
Yankees relievers have a 1.60 ERA over the past 21 games.
"The bullpen's been incredible," Rasner said. "Some things are coming together."
Rodriguez hit a leadoff double in the second and scored on a one-out single by Cano, who is 12-for-23 since the All-Star break. The second baseman is batting .339 after the break for his career.
"Lucky," he said. "I'm doing the same things."
Cano's father, Jose, who pitched briefly for the Houston Astros in 1989, threw to him last Wednesday back home in the Dominican Republic and the two worked on game situations.
"I feel like I'm staying behind the ball, not reaching or jumping like I was in the first half," Cano said.
The error was charged to Giambi, who later made a nice play on Jason Kubel's RBI groundout.
Minnesota RF Michael Cuddyer, sidelined since June 28 with a strained tendon in his left index finger, had a CT scan on his knuckles that did not reveal a tear. Twins doctors will determine a course of treatment, and the team isn't sure when he'll be able to return. ... Gardenhire dropped the slumping Gomez from the leadoff spot to No. 9 in the order. ... Yankees C Jorge Posada had his injured throwing shoulder examined by New York Mets medical director Dr. David Altchek. The Yankees said they hoped to have information Wednesday on whether Posada will need season-ending surgery. ... Girardi said he hopes Damon, just back from a left shoulder injury, might be able to play the outfield this weekend in Boston. ... Farnsworth, who has 10 straight scoreless appearances, has held opposing batters hitless in their past 28 at-bats -- a span of nine innings.