Martin Hanzal replied for the Coyotes.
Canucks goaltender Roberto Luongo picked up his first win of the pre-season as he played the full 60 minutes, recording 21 saves while rarely tested. Luongo saw his first action since allowing four goals in the first 12:24 in a 4-1 loss to Edmonton last Thursday.
The Canucks, featuring mostly veterans, controlled play throughout the game against a Phoenix squad that iced several prospects.
Higgins opened the scoring 16:29 into the game as he fired in a shot off a face-off after Ryan Kesler won the draw.
Hansen's power-play goal just over two minutes later put the Canucks ahead 2-0.
Hanzal reduced Phoenix's deficit to 2-1 on a power play 1:34 into the second period as he deflected David Rundblad's centring pass through Luongo's legs.
Weber, who turned 25 on Monday, put the Canucks ahead 3-1 with a slapshot from the point at the 11-minute mark of the second period. It was the third point in three pre-season games for Weber, a Morges, Switzerland native who signed as a free agent in July after five seasons with the Montreal Canadiens organization.
He recorded only two assists in six games with the Canadiens last season.
Santorelli scored his second goal in two straight pre-season games, improving his chances of sticking as a third or fourth-liner.
Top 2013 draft picks Hunter Shinkaruk (24th overall) and Bo Horvat (ninth overall) earned assists on the goal. Horvat's helper was his first point of the pre-season while Shinkaruk recorded his third point.
He picked up another one as he set up Sestito's goal with just under 12 minutes gone in the third, which put the Canucks up 5-1.
Notes: Canucks winger Zack Kassian was suspended Monday for the rest of the pre-season and the first five games of the regular season for a high-sticking incident against Edmonton centre Sam Gagner on Saturday. Gagner suffered a broken jaw on the play and is out indefinitely. ... Vancouver winger Dale Weise was suspended for the rest of the pre-season for a hit to the head on Taylor Hall in the same game. ... Phoenix captain Shane Doan and centre Mike Ribeiro were among Coyote regulars who sat out. ... Vancouver's Daniel and Henrik Sedin were used as penalty-killers. ... Former Vancouver Giants star Gilbert Brule is getting a chance at a second stint with the Coyotes. Brule, the sixth overall pick by Columbus in 2006, is on a professional tryout with Phoenix, where he spent 33 games in the 2011-12 season following a trade from Edmonton. He toiled in Switzerland for 14 games last season. ... Vancouver's David Booth remained sidelined with a groin injury that he suffered Saturday in the morning skate prior to the game against Edmonton. Booth was slated to make his return in that game from an ankle injury that had kept him out since March. But the groin injury kept him off the ice.
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