The win was their first road victory of the season.
Christian Dvorak scored twice and Conor Garland also scored for Arizona.
Darcy Kuemper made 38 saves for the Coyotes.
Mark Scheifele had a goal and an assist for the Jets.
Kyle Connor got the other Winnipeg goal.
Josh Morrissey had a pair of assists.
Connor Hellebuyck stopped 31 shots and took the loss for the Jets, who lost their second straight home game as they were pasted by Pittsburgh 7-2 on Sunday night.
Mark Scheifele got the Jets on the board with a power play marker 7:35 into the opening period when he snapped a puck past Arizona goaltender Darcy Kuemper after Patrik Laine rocketed a shot off the goal post to score his 4th of the season.
Conor Garland drew the Coyotes even when he deflected a puck past Winnipeg goaltender Connor Hellebuyck with eight seconds remaining in the first.
Winnipeg ran into penalty trouble in the second period and Arizona took full advantage, scoring twice on the power-play over a two minute span.
Arizona took the lead on a power play early in the second when Christian Dvorak was credited with a goal as it was redirected by Jet defenceman Josh Morrissey past the Winnipeg goaltender at 5:11.
Nick Schmaltz made it 3-1 at 7:21 when he moved in from the right face off circle after working a give-and-go with Jordan Oesterle before snapping a puck past Hellebuyck give Arizona a two-goal lead.
Dvorak scored again at 17:47, moving in from just under the right faceoff hash mark before beating Hellebuyck with a high wrister just under the cross bar after Schmaltz hit him with a crisp pass from the blue line.
The goal was his second of the season.
Kyle Connor scored a power play marker just under five minutes into the third.
With Conor Garland off for high sticking, Connor lifted a backhander over Kuemper's glove at 4:58 after Mark Scheifele hit him with a crisp pass along the red line to the right of the Arizona goaltender.
The goal was his third of the season.
SHOTS-ARIZONA 35 WINNIPEG 40