Sven Baertschi had two goals, Adam Gaudette scored and Jacob Markstrom made 18 saves for Vancouver (20-21-5), which has lost three in a row (0-2-1) despite outshooting Arizona 31-15 over the final two periods and overtime.
"We easily could have run away with it," Baertschi said "It wasn't the prettiest game. We hung around and had a chance to win it really in the third. Too bad we came up short."
Garland gave the Coyotes a 3-2 lead at 9:57 of the third period off a backdoor pass from Alex Galchenyuk. After Gaudette turned it over at the Canucks blue line, Galchenyuk collected the puck and spun around Ben Hutton before finding Garland at the right post.
"The whole bench was yelling (at Galchenyuk) to shoot but he saw something there and Garland is by the net again and he gets that tap in," Tocchet said. "Give the kid credit, he's got six goals (on the season) and a lot are around the net."
Baertschi scored on a rebound at the left post to tie it 3-3 at 15:35.
Vancouver, which had had been shut out in the previous two games and three of its past four, didn't get a shot on goal until 15:27 of the first period.
Panik scored to make it 1-0 at 1:26 of the second period after receiving a spinning backhand pass from Hinostroza from behind the net and scoring with a quick blocker-side shot.
"As a line we played really good. We are hard on their D and we make some plays in their zone," Panik said. "[Brad Richardson] and [Hinostroza] did a really good job so it helped me a lot."
Baertschi scored 57 seconds later to tie it 1-1. After skating in on a partial breakaway, he pulled up, put the puck between the legs of Chychrun, and scored with a wrist shot under Kuemper's blocker.
"We got the lead a couple times and Vancouver scratched and clawed to get back in it," Tocchet said.
Cousins made it 2-1 at 9:55 when Panik's initial shot deflected in off his skate at the top of the crease.
Gaudette tied it 2-2 at 19:27. Hutton's point shot was blocked by Antoine Roussel in front, but the puck bounced to Gaudette, who scored at the left post. It was his first game with Vancouver since being recalled from Utica of the American Hockey League on Jan. 8.
"I feel a little more confidence out there, a little more swagger," Gaudette said. "Being down there, it was great, and hopefully this just keeps rolling."
