Martin Hanzal replied for the Coyotes.
Canucks goaltender Roberto Luongo picked up his first win of the preseason, recording 21 saves while rarely being tested in 60 minutes. Luongo saw his first action since allowing four goals in the first 12:24 in a 4-1 loss to Edmonton last Thursday.
Higgins opened the scoring 16:29 into the game and Hansen followed with a power-play goal 2:04 later.
Hanzal answered with a power-play goal at 1:34 of the second, but it was all Vancouver after that.
Thomas Greiss went all the way for Phoenix, stopping 28 shots.