Eakin, a Winnipeg native, was acquired by the Jets from the Vegas Golden Knights three days before the NHL trade deadline for a conditional 3rd round pick.
The goal was his 5th of the season and first as a Winnipeg Jet.
After winning a faceoff back to Patrik Laine, Eakin drove the net as the Finnish winger fanned on his shot attempt.
He did manage to get the disc through to Ehlers in the high slot and he managed to kick it ahead to Eakin who was patient with the puck before beating Kuemper with a backhand shot to clinch the win for Winnipeg.
The win moved the Jets back into a wild card playoff spot with 78 points.
Nikolaj Ehlers paced the attack for the homeside with a goal and two assists.
Tucker Poolman had a goal and an assist.
Mark Scheifele also scored for the Jets, who moved to 36-28-6.
Connor Hellebuyck turned aside 36 shots for Winnipeg.
Nick Schmaltz fired a pair of goals for Arizona, who closed out a three-game road trip with a loss, their second straight.
Phil Kessel had a pair of assists for the Coyotes.
Darcy Kuemper made 30 saves for the Arizona, who dropped to 33-29-8.
The Jets welcomed Adam Lowry back into the lineup after a 20 game abscence and the physical centreman made his impact felt early, getting into a one sided fight with Arizona's Lawson Crouse and dropping him to the ice just over two minutes into the contest.
The Coyotes took a two-goal lead before Winnipeg stormed back with four straight markers to post the win.
There was no scoring until the final five minutes of the period when Nick Schmaltz got Arizona on the board at 15:50.
Schmaltz took a hard cross ice feed from Phil Kessel before cutting to the slot and snapping a wrister past Connor Hellebuyck, beating the Winnipeg goaltender high blocker side.
Schmaltz scored his 2nd of the night with two seconds remaining in the first when he hustled to the net and got his blade on a rebound off a Phil Kessel shot, lifting the disc past Hellebuyck's outstretched glove to make it 2-0 Coyotes.
The goal was his 11th of the season.
Nikolaj Ehlers cut the lead in half 2:13 into the second when Tucker Poolman hit him with he broke into the Arizona zone, bursting past () and beat Darcy Kuemper with a high wrister to make it 2-1.
The goal was his 25th of the season.
Tucker Poolman tied the contest 17:27 into the second when he converted a rebound off a Cody Eakin shot past Kuemper to make it 2-2.
The goal was his 4th of the season.
Cody Eakin gave the Jets the lead at 11:33 of the third off of a faceoff.
Mark Scheifele added an empty netter late in the third to clinch the win for the Jets.
The goal was his 29th of the season.
Winnipeg travels to Edmonton to face the Oilers on Wednesday while Arizona hosts Vancouver on Thursday.
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