Cooke saw a loose puck sitting below the goaltender and drove the net after Torrey Mitchell took a sharp-angle shot from along the goal line.
"We want to be at the net," Cooke said. "We want to go to the net. We want to go to those tough areas. I want to be there as much as I can. (Mitchell) did a great job of getting the puck there. It was loose. I saw it the whole time and the whistle didn't go."
The Wild continued their dominant play by carrying the pace of the game, possessing the puck more often, getting more shots and creating more scoring chances then their opponents. The Wild have done all four in each of the team's four games to start the season.
"We want to be a puck possession team," Cooke said. "We want to spend time in the offensive zone. We want to grind teams down.
"If we're shooting the puck and playing in the offensive zone, then they can't be doing it in our end."
The Wild (1-1-2) were able to the control the pace and tempo of the game by winning nearly 75 percent of the faceoffs.
"We never start with the puck," Jets head coach Claude Noel. "We chased it pretty much the whole night.
"We don't start with it, so we're always checking. We're always chasing it down."
Jonas Brodin got the scoring starter seven minutes and 39 seconds into the opening period by driving the net. Cooke's shot from the top of the circles was stopped, but the rebound glanced up and went into the net off Brodin. The play went under review, but remained a goal.
The Jets (2-2-0) were able to tie the game before the first intermission with the help of two Wild penalties four seconds apart.
Bryan Little tipped a shot from the point by Tobias Enstrom under Josh Harding while on the two-man advantage.
The Wild return to action Saturday against the Dallas Stars at the Xcel Energy Center.
No. 3 – Ondrej Pavelec. The Jets goaltender stopped 28 shots.
No. 2 – Jonas Brodin. The Wild defenseman scored a goal.
No. 1 – Matt Cooke. The Wild forward recorded a goal and an assist.
Winnipeg.…..1 0 0 – 1
Minnesota…..1 1 0 – 2
First Period – 1, Minnesota, Brodin 1 (Cooke, Brodziak), 7:39. 2, Winnipeg, Little 3 (Enstrom, Byfuglien), 19:17 (pp). Penalties – Byfuglien, WPG (roughing), 6:42; Byfuglien, WPG (roughing), 6:42 Stoner, MIN (hit to the head), 6:42; Stoner, MIN (roughing), 6:42; Stuart, WPG (tripping), 13:41; Little, WPG (hooking), 15: 36; Brodin, MIN (holding), 18:31; Brodziak, MIN (hooking), 18:35.
Second Period – 3, Minnesota, Cooke 2 (Mitchell, Stoner) 10:30. Penalties – Ladd, WPG (hooking), 7:12; Veilleux, MIN (holding) 16:12; Byfuglien, WPG (interference), 19:53.
Third Period – None. Penalties – Ballard, MIN (interference), 3:24; Enstrom, WPG (hooking), 3:52; Jokinen, WPG (tripping), 11:04; Brodin, MIN (cross checking), 13:33.
Shots on goal – Winnipeg 6-4-5 15. Minnesota 10-12-8 30.
Goalies – Winnipeg, Pavelec (28-30). Minnesota, Harding (14-15). A – 17,366. Referees – Ghislain Hebert, Dan O'Rourke. Linesmen – Brad Lazarowich, Brad Kovachik.