J.T. Miller had a goal and an assist, Quinn Hughes had three assists, and Collin Delia made 24 saves for Vancouver (38-37-7), which won four of its final five games.
"It was kind of a weird game," Tocchet said. "I thought the Coyotes worked really hard, especially in the second and third [periods]. We got the win, but it was one of those games where I think both teams wanted to get the season over with."
Liam O'Brien scored twice, Nick Schmaltz had a goal and an assist, and Karel Vejmelka made 19 saves for Arizona (28-40-14), which lost 11 of its final 12 games (1-8-3).
"We wanted to be as professional as possible and keep your focus on the game and play 82 games, not 81 or 80," Coyotes coach Andre Tourigny said. "I'm really proud of the way we battled, the boys they never quit; and it would have been easy tonight, they were down (4-1) early."
O'Brien cut it to 4-3 at 9:54 of the second when he deflected a point shot by Michael Kesselring, who had two assists for his first NHL multipoint game.
Schmaltz tied it 4-4 at 16:40 of the third, scoring from the left face-off dot through a screen.
"We came back from 4-1 and I thought we had control of the game too, so it's kind of tough to lose that one in overtime," O'Brien said.