Bryzgalov, who is rarely short of words off the ice, was taunted a few times by the home crowd with chants of "Il-Ya!" He answered the catcalls with a series of arm gestures.
"I want to show them, 'Get louder!' " said Bryzgalov, who Minnesota acquired at the trade deadline from Edmonton. "It sounds like a good tradition. It became a good tradition every time I play here."
"Mikko (Koivu) made a nice pass down to Zach and Zach just put it through a guy and found me," Coyle said. "And I just tried to throw it on net and it happened to go in, so it was a great play by those guys."
The Wild (41-26-12) closed in on a playoff berth in the Western Conference with the win. Minnesota would need to lose its final three games with Phoenix winning four straight in order for the Wild to miss the playoffs.
Bryzgalov wasn't bothered by the crowd while earning his fourth shutout of the season. He also improved to 6-0-3 since joining his new club.
"They keep the game simple for me, let me see the shots," Bryzgalov said of his new teammates. "They block a lot of shots. I just go on the ice and play hard to try to give the team a chance to win the game. The guys play in front of me unbelievable."
The Jets' Michael Hutchinson, a 24-year-old rookie who began the season in the ECHL, made his first career NHL start with regular backup Al Montoya still dealing with a lower-body injury. His only blemish on 17 shots came on Coyle's one-timer.
"I thought I played pretty well," Hutchinson said. "There's some times where nerves get the best of you and you start overthinking certain situations, but overall I think I gave the team a chance to win the game."
Neither team could generate much offense through the first two period, with the Wild leading in shots 13-12. The third period was wide open by comparison, with Winnipeg sending 12 pucks at Bryzgalov. But even four power-play chances couldn't help the Jets find the back of the net.
"Whenever your goalie is giving you performances like that, your penalty kill is going to be better," Wild coach Mike Yeo said.
Winnipeg forward Evander Kane, a healthy scratch Saturday night in Toronto for reportedly being late to a team meeting, was back in the lineup. He managed just one shot on goal and was on the ice for Coyle's goal.
"Special teams is what won the game tonight," Kane said. "It's tough when you lose 1-0, because you've got to score at least one to win."
The Jets wrap up their home schedule Thursday night against Boston, and finish their season the next night in Calgary. Minnesota returns home to face Boston, St. Louis and Nashville.
Jets captain Andrew Ladd missed his first game due to injury since the 2010-11 season, while Dustin Byfuglien (torn muscle) is done for the season. ... Still on the Jets' injured list were forwards Chris Thorburn and Mark Scheifele and defensemen Keaton Ellerby and Zach Bogosian. ... Minnesota was without forwards Mikael Granlund and Jason Zucker and defensemen Clayton Stoner and Keith Ballard. ... Jets center Jim Slater played in his 500th career NHL game.