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 a taunting crowd as the trade-deadline pickup from Edmonton earned his fourth shutout of the season.
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.
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.
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.
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.
NOTES: 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.