Mariano Rivera allowed a Baltimore run in the ninth, but held on to claim his 43rd save and moved the Yankees into third place in the American League East, a half game in front of the Orioles.
The evening began with Tampa Bay, New York, Baltimore, Cleveland and Kansas City all separated by just 2 1/2 games in the race for the second wild card position in the American League.
It was a 3-3 tie heading into the ninth, but Cano led off the inning with a home run against Tommy Hunter (4-4). One out later Curtis Granderson tripled and he scored on a two-out, infield single by Lyle Overbay for a 5-3 cushion.
Rivera then struck out Manny Machado swinging to end the game.
Reliever David Robertson (5-1) was credited with the win after working out of a jam in the eighth.