Alexi Casilla had three hits for the Twins, but his throwing error led to three unearned runs in New York's four-run second inning.
Minnesota dropped to 3-17 at Yankee Stadium since the start of the 2002 season, losing the opener of its final regular-season series at New York's longtime home. The Twins have lost six straight series in the Bronx.
Nick Blackburn (7-6) lasted just 1 2-3 innings in his second career start against the Yankees, allowing seven hits and six runs, three earned.
Blackburn also had an early exit in his first game against New York, departing after he was drilled in the face by Bobby Abreu's line drive in the fifth inning. The rookie right-hander, who allowed just one run in that June 1 start, was left with a swollen lip and headaches but still managed to make his next scheduled start against the Chicago White Sox.
New York played without longtime catcher Jorge Posada, who was placed on the 15-day disabled list with an injured throwing shoulder and could be headed for season-ending surgery. Posada was scheduled to see New York Mets medical director Dr. David Altchek on Tuesday to get an MRI and have his shoulder examined.
Posada said he would make a decision on surgery after talking over his options with Altchek.
"It's just really, really tough," he said. "Right now, I'm going through tough times."
Johnny Damon was activated from the disabled list and went 1-for-4 serving as the designated hitter for New York (54-45), which improved to a season-best nine games over .500. Jose Molina was behind the plate, and he snapped an 0-for-14 skid with a second-inning single and had a season-high three hits.
The Yankees chased Blackburn in the second. With the bases loaded and one out, Damon hit a grounder to second baseman Casilla, who bounced his throw to the plate. Melky Cabrera scored to give New York a 3-2 lead.
Jeter followed with an RBI single to left, Abreu drove in a run with a fielder's choice and Rodriguez singled in Damon on Blackburn's final pitch of the night.
That was enough for Sidney Ponson (6-1), who allowed three runs and nine hits in 5 2-3 innings. The right-hander improved to 2-0 in four starts since he signed a minor league deal with the Yankees on June 18.
Casilla, Carlos Gomez and Jason Kubel each drove in a run for the Twins (55-44), who dropped to 23-9 since June 13. Denard Span had three hits.
Rodriguez's first-inning homer was his 21st of the season and Cano's drive to right leading off the third was his eighth of the year. Jeter led off the sixth with his sixth homer to make it 9-3.
