Arizona opened the season with six straight road games before returning to the desert and The Mullett.
Mullett Arena, Arizona State University's new arena, is by far the smallest venue in the NHL and a temporary home until a permanent one is built.
The Coyotes had the early jump in front of 5,000 mullet-wearing fans — headbands with long locks were the giveaway — going up 2-0 on Christian Fischer's first-period goals.
The Jets whittled their way back.
David Rittich, who stopped 19 shots, made a couple of nice saves to start overtime, and Wheeler beat Karel Vejmelka on a one-timer after Pierre-Luc Dubois created a 2-on-1 after stealing the puck from Shayne Gostisbehere.
Vejmelka had 32 saves.
The Coyotes got off to a great start.
Fischer scored the first NHL goal in Mullett Arena history midway through the first period, when Troy Stecher's shot from the right circle hit him shoulder and caromed pass Rittich.
Fischer also had the second goal, beating Rittich glove side off a faceoff win.
The Mullett momentum didn't last long.
Perfetti scored 26 seconds later after pickpocketing Josh Brown along the boards, flipping a shot over a prone Vejmelka following some nifty stickhandling.
Rittich and Vejmelka stole the show in the second period, each making difficult close-range saves through traffic.
Scheifele tied it with his sixth goal of the season midway through the third, whipping in a rebound after Vejmelka got jammed on a high shot.
Winnipeg is 0 for 14 on the power play — 0 for 5 Friday — the past four games and 2 for 24 overall. ... Coyotes D Jakob Chychrun missed his seventh straight game after suffering a recent setback in his recovery from offseason wrist surgery. ... Jets D Logan Stanley missed his second straight game after getting banged up on a blocked shot Monday against St. Louis.
Jets: At at Vegas on Sunday.
Coyotes: Host the New York Rangers on Sunday.
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John Marshall, The Associated Press