Cano's monstrous shot into the second-deck in right field erased a 2-0 Yankees deficit and sent New York on its way to a victory in the opener of a three-game series.
Ivan Nova (1-1) earned the win after yielding two runs over five innings, striking out six while walking two.
Mariano Rivera tossed a perfect ninth to collect his third save as New York won its sixth in seven games.
Brandon McCarthy (0-2) was tagged with the loss, surrendering three runs on nine hits through four innings.
Cody Ross led the D-backs at the plate, going 2-for-4 with an RBI single.