Cano hit two-run blasts in both the second and third innings off Johan Santana, who threw the first no-hitter in Mets history when he last started June 1.
Nick Swisher and Andruw Jones hit solo homers off Santana in the third and Swisher contributed an RBI double during the Yankees' three-run seventh.
Kuroda (5-6) retired the first 10 men he faced before Josh Thole reached on a fielding error by shortstop Derek Jeter. Thole was immediately erased in a double play.
The only hit off Kuroda came in the sixth when Omar Quintanilla reached on a two-out double.
The Mets had just one other hit in the game, that coming when Lucas Duda doubled home Quintanilla in the ninth with Ryota Igarashi on the mound.
Santana (3-3) gave up six runs on seven hits in five innings.