The Yankees held their breath after captain Derek Jeter was hit on the left hand by a pitch from Orioles reliever Jim Miller leading off the ninth inning, forced to leave the game.
X-rays were negative, and Jeter said that there was no question he would play in Sunday's finale.
"I'm going to play tomorrow," Jeter said. "I'm sure it's going to be a lot of fun. I think a lot of the guys will get here early and take it all in."
Attended to on the field by manager Joe Girardi and assistant trainer Gene Monahan, Jeter left the game as the sellout crowd of 54,662 booed Miller lustily. Pinch-runner Brett Gardner stole second base and moved to third when on a fielder's choice.
After a strikeout and an intentional walk, Cano came through with the winning hit off Jamie Walker, setting off a celebration between first and second bases on the infield and giving the Yankees their seventh win on Yankee Stadium's final homestand.
"You do it for the fans and thank the Yankees fans for their support, showing up every day to the ballpark," Cano said. "I can't wait to see tomorrow."
Winners of four straight games to improve to 13 games over .500, the Yankees can set a new high-water mark for the season and script the ending of a series sweep on Sunday, sending Andy Pettitte on the mound.
"I think this building should close on a win," Girardi said. "I think that's what this building is used to doing."
Making his third Major League start, Alfredo Aceves continued to offer the Yankees ammunition to ponder for their future rotation needs. The 25-year-old Mexican League product scattered five hits in six scoreless innings, walking three and striking out three.
In 26 innings at the big league level, Aceves has allowed just four runs, as the Yankees continue to consider his audition.
"He's thrown very well the month of September, and he's been in some big situations," Girardi said. "He's faced some tough opponents -- clubs that are fighting for something. 'Ace' has thrown the ball extremely well."
Aceves turned an unassisted double play in the first inning on a bunt popped up by Adam Jones, jogging to second base to double off Brian Roberts.
Aceves' toughest challenge came in the sixth inning, with his pitch count rising to an eventual total of 92 and two runners aboard. Aceves induced Luke Scott to bounce into an inning-ending fielder's choice, completing his afternoon.
"With runners in scoring position, he was able to make big pitches," Girardi said. "His ability to control the running game and field his position. ... There's a lot of things that this young man does right besides throwing strikes and having good stuff. He takes care of the other parts of the game, too."
Seeking his first victory since July 11, Baltimore left-hander Brian Burres held the Yankees scoreless through seven innings, limiting the bats to just three hits while walking none and striking out two.
He could do no better than a no-decision, however, handing the ball off to Miller for the eighth.
Brian Bruney worked around a hit and a walk in the seventh inning, and Damaso Marte pitched a perfect eighth. Mariano Rivera set the Orioles down in order in the ninth inning, recording the last out by getting Alex Cintron looking at a called third strike.
The victory kept New York mathematically alive in the postseason discussion. Any combination of Yankees losses and Red Sox victories adding to two would finalize the Yankees' first playoff absence since the strike-shortened 1994 campaign.
"It's a must-win for this club, because of where we are in the standings," Girardi said. "We're still alive. That's all you can ask -- to stay alive and make those games in Boston really mean something."