The Coyotes are 7-1-1 in their last nine games and 20-12-2 overall in their first season under coach Dave Tippett.
"We really expected to win," said Coyotes captain Shane Doan, adding the players knew they were going to be competitive despite the team's uncertain future.
"Tippett knows what he wants to do and was able to dictate exactly what everybody wants and that really makes it easy."
Prucha opened the scoring in the first period, taking pass at the side of the crease and wiring a shot short-side past Vesa Toskala.
Some sloppy defensive play by Toronto allowed Prucha to put his team up 2-0 just 51 seconds into the second, but exactly a minute later Mayers got that one back on a breakaway started by defenseman Francois Beauchemin.
However, Phoenix took over with three straight goals.
"They were kind of swarming everywhere, in our zone and in their zone and they made us look pretty bad," Maple Leafs defenseman Jeff Finger said. "No bounces went our way and they got a few their way."
Fiddler backhanded home a loose puck that came to rest in the slot before Bissonnette tipped home a point shot from Yandle to make it 4-1.
"I was pretty excited and I look forward to talking to my dad after the game," Bissonnette said. "It was his first NHL game."
Upshall was credited with his goal when the puck went through the Toronto goalmouth, deflected off Ian White's skate and trickled over the line before Toskala could smother it with his glove.
Kessel scored a late second-period power-play goal before Ponikarovsky brought the score the Maple Leafs to 5-3 from the high slot in the third.
The loss ended a four-game home winning streak for Toronto, while the Coyotes earned their fourth consecutive victory over the Leafs.
Doan played his 999th game. ... Toronto defenseman Luke Schenn was a healthy scratch for the third straight game. ... The game was Phoenix's first in Toronto since Jan. 14, 2006.
Copyright by STATS LLC and The Associated Press
Arena: Air Canada Centre Location: Toronto, Ontario
Referees: Kevin Pollock, Brian Pochmara Linesmen: Mark Pare, Anthony Sericolo
Attendance: 19,088 (101.5% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Petr Prucha (5)
(Power Play) Assists: Keith Yandle, Martin Hanzal
Petr Prucha (6)
Assists: Martin Hanzal, Radim Vrbata
Jamal Mayers (1)
Assist: Francois Beauchemin
Vernon Fiddler (4)
Assists: Daniel Winnik, Keith Yandle
Paul Bissonnette (2)
Assists: Keith Yandle, Daniel Winnik
Scottie Upshall (10)
Assists: Matthew Lombardi, Lauri Korpikoski
Phil Kessel (13)
(Power Play) Assists: Matt Stajan, Alexei Ponikarovsky
Alexei Ponikarovsky (13)
Assists: Matt Stajan, Mike Komisarek
Radim Vrbata (11)
(Empty Net) Assist: Martin Hanzal