It wasn't as easy for the Wild as it was for the first six games - all six were multiple-goal victories.
The Wild (20-10-2) were expected to win easily against a team that has now lost seven straight.
"You always expect a tough game," Mikko Koivu said. "I don't think we were able to play as good as we can. Sometimes that happens when you come from the road and come home. Good teams find ways to win hockey games and we did that tonight."
The Wild owned the overtime session with all five shots on goal and control of the puck in the offensive zone - a penalty 35 seconds in will do that.
Eight seconds after the completion of the power play, Koivu slid a puck under Jason LaBarbera for the win.
"(It was late in the power play) you always want to take it to the net," Koivu said. "(Zach Parise) tried it first and they blocked that shot. He gave it to me and I had a chance to take it to the net. I did and it went in."
After a sluggish period and a half, Ryan Suter tied the game with 54.3 seconds remaining in the third period with a shot through traffic and over the arm of LaBarbera.
"(Koivu) made a good play to get the puck back to (Jared Spurgeon)," Suter said. "(Spurgeon) made a good pass to me and I had a lot of time. (Parise) was in front taking away (LaBarbera's) eyes and you can't really ask for anything more than that."
Torrey Mitchell slid a rebound past LaBarbera at the 15:15 mark of the first period to get the Wild on the board first. It was the 10th time in the last 11 games the Wild scored first.
The Wild extended the lead when Matt Cullen knocked a clearing attempt by LaBarbera out of the air and fired it into the open net.
On ensuing face-off following the Cullen, Konopka dropped the gloves with the Coyotes' Kyle Chipchura.
From there, the Coyotes dominated play.
The Wild got knocked back on their heels and could not right themselves until the final minute.
"You get up two goals and we're on a winning streak. You think you are just going to put things in cruise control," Mitchell said. "Every team is good and anyone can beat anyone."
The Coyotes got two quick goals late in the second period from Rob Klinkhammer and Boyd Gordon. Michael Stone then gave the Coyotes its only lead 55 seconds into the third period.
"We battled back for a point," Coyotes coach Dave Tippett said. "Reality is in our situation we need more than one point. That's just calling a spade a spade here."
The Coyotes' trio of goal scorers entered the game with a combined five goals - Klinkhammer led the way with three.
No. 3 – Rob Klinkhammer. The Coyotes forward recorded a goal and an assist
No. 2 – Mikko Koivu. The Wild forward scored a goal and added an assist.
No. 1 – Ryan Suter. The Wild defenseman scored a goal.
Phoenix……..0 2 1 0 – 3
Minnesota…..1 1 1 1 – 4
First Period – 1, Minnesota, Mitchell 3 (Rupp, Stoner), 13:15. Penalties – Hanzal, Phx (tripping) :30; Moss, Phx, major (fighting), 3:25; Falk, Min, major (fighting), 3:25.
Second Period – 2, Minnesota, Cullen 6 (unassisted), 5:29. 3, Phoenix, Klinkhammer 4 (Gordon, Moss), 11:14. 4, Phoenix, Gordon 1 (Yandle, Moss), 14:28. Penalties – Chipchura, Phx, major (fighting), 5:32; Konopka, Min, major (fighting), 5:32; Falk, Min (elbowing), 6:16; Doan, Phx (goaltender interference), 7:36; Klesla, Phx (interference), 15:44.
Third Period – 5, Phoenix, Stone 3 (Doan, Klinkhammer), 1:52. 6, Minnesota, Suter 3 (Spurgeon, Koivu), 19:05. Penalties – Gilbert, Min (tripping), 9:54.
Overtime – 7, Minnesota, Koivu 9 (Parise, Brodin), 2:43. Penalties – Vermette, Phx (cross checking), :35.
Shots on goal – Phoenix 10-9-8-0 27. Minnesota 8-14-10-5 37.
Goalies – Phoenix, LaBarbera (33-37). Minnesota, Backstrom (24-27). A – 19,076. Referees – Dennis LaRue, Brad Meier. Linesmen – John Grandt, Brad Lazarowich.