Pyatt scored 5:52 into the final frame and Ilya Bryzgalov made the lead hold up the rest of the way, stopping seven third-period shots for the Coyotes, who won their sixth straight game.
Pyatt also found the net in the second period. Scottie Upshall got the other goal for Phoenix and Bryzgalov turned aside 25 of 27 scoring attempts to earn the victory.
The Canucks dropped their second straight home contest after absorbing a 7-1 beating by Chicago Saturday.
Christian Ehrhoff and Tanner Glass got Vancouver's goals and Roberto Luongo stopped 25-of-28 shots.
Notable deaths of 2014 [PHOTOS]