The game was rescheduled from May 19, when the Yankees and Blue Jays were rained out.
Cano's four hits included a three-run home run -- the 200th homer of his career -- in the third inning that started New York's comeback from a 4-0 deficit. He added an RBI double in the seventh.
New York starter Ivan Nova (7-4) allowed four runs and nine hits in 6 1/3 innings but was saved by two three-run home runs -- Cano's in the third and one by Chris Stewart in the sixth that put the Yankees ahead.
Blue Jays starter Esmil Rogers was unable to hold the early lead but escaped with a no-decision. Neil Wagner (2-4) allowed the home run to Stewart and took the loss.
The Blue Jays used a four-run second inning, capped with Rajai Davis's two-run double to take the lead but Cano's home run to dead center cut into it and Stewart's shot down the left-field line wiped it out.
Suzuki's double and single on the day moved him to 3,999 hits for over his 22-year career in Japan and the United States.