Derek Morris scored the go-ahead goal three seconds into a power play at 12:12 of the first period. Jeremy Roenick added what might be his final NHL goal, an empty-netter, with 21.2 seconds to play.
Roenick and goalie Curtis Joseph both drew standing ovations from the crowd after the final goal.
Roenick, whose goal was his 11th of the season, said he will decide this summer whether to retire from the game.
Despite the victory, the Coyotes completed their worst season since the franchise moved from Winnipeg in 1996.
Vancouver, on the other hand, had clinched the Northwest Division title with a victory at San Jose on Saturday. The Canucks, who set franchise records for wins and points, start the playoffs at home against Dallas on Wednesday.
The Coyotes finished last in the Pacific Division for the third year in a row, the last two with Wayne Gretzky as coach. They were last in the Western Conference for the first time since the franchise moved from Winnipeg. Phoenix's 67 points were fewest for the team since its move from Canada.
The futility fuelled speculation that general manager Mike Barnett, Gretzky's good friend and former agent, might be fired in the coming days. Gretzky's job is safe and he plans to return.