Playing what is almost sure to be the penultimate game at Yankee Stadium, New York got a perfect inning from Mariano Rivera (6-5) and a fine start by impressive rookie Alfredo Aceves.
But it was a painful victory. Jeter left after getting hit on the hand by a pitch in the ninth, which started the winning rally.
X-rays were negative and he said he'll play in the ballpark's farewell game Sunday night.
"I don't need to ask," manager Joe Girardi said. "It's not broken. It's sore."
The Red Sox lost 6-3 in Toronto, so the Yankees cut Boston's AL wild-card lead to 6 1/2 games with seven to play.
A New York loss combined with a Boston win would have knocked the Yankees out of contention, assuring they'd miss a postseason for the first time since 1993. New York's run of 13 straight playoff berths began in '95, a year after a labor dispute between players and owners led to the postseason being canceled.
So the Yankees are still alive - barely. They could be eliminated Sunday with a loss and a Boston win, which would put a damper on all the festivities planned for the 85-year-old ballpark in its regular-season finale.
"It's a must-win for this club because we are still alive," Girardi said. "You want a win because that'll close out the building and that's significant."
Andy Pettitte will pitch for the Yankees before a national television audience. Next season, New York will move into a $1.3 billion palace being built across the street.
"One of the things that you learn very young is about the history and tradition, so I'm very happy Andy's starting," Jeter said.
Brian Burres was even better than Aceves, shutting down the Yankees on three hits through seven innings. The lefty walked none in his first start since Aug. 31.
Jim Miller (0-2) struck out two in a 1-2-3 eighth before plunking Jeter on the left hand to begin the ninth. Jeter jumped away in pain, then let his arm dangle by his side as he was checked by a trainer.
Quickly removed from the game, Jeter tossed his helmet in the dugout before disappearing up the runway - a rare display of frustration for one of baseball's most poised players.
"It doesn't feel good," he said.
Jeter was hit on the same hand by a pitch from Baltimore's Daniel Cabrera in May. The Yankees' captain wears a protective pad on the outside of his batting glove, but he appeared to get hit flush.
Pinch-runner Brett Gardner stole second and Bobby Abreu was intentionally walked. Alex Rodriguez hit a potential double-play grounder to second, but shortstop Juan Castro's relay to first was wide.
A-Rod swiped second as Jason Giambi struck out against Jamie Walker, and Xavier Nady was intentionally walked to load the bases.
Benched earlier in the week for not hustling on defense, Cano lined Walker's next pitch on one hop into center and was mobbed by excited teammates on the infield. By the time the ball reached the outfield, Walker had slammed his glove to the ground.
"I've never done that. I apologize for that," Walker said. "I'll have to deal with my kids on that one."
The 25-year-old Aceves yielded five hits over six innings in his third major league start, all strong outings this month. New York has won four straight and seven of eight.
The Orioles dropped to 2-19 in their last 21 one-run games and have lost 24 of 31 overall.
"I'll take the good starting pitching every time," manager Dave Trembley said. "Obviously, it's been an area where we have been improving. That's a real positive. I have no problem with the effort that this team has been displaying every night."
