The teams had combined for only 28 shots when Pominville collected Mikko Koivu's pass in the crease and pushed it past a helpless Ray Emery 3:52 into the third period.
On the ensuing shift, Coyle tapped a rebound off Jared Spurgeon's slap shot into an empty corner at 4:49.
It was an impressive and unexpected flurry in a game that had played out as the statistics predicted. When the puck dropped, the Wild's 17 even-strength goals allowed in 21 games led the NHL; and the Flyers had allowed two or fewer goals in 10 of their past 14 games.
Plus, the Wild had scored only six goals in their five previous games (1-3-1). But Minnesota controlled most of the action, even if its chances were minimal, to improve to 11-3-2 at home.
Goaltender Josh Harding improved to 11-1-0 at Xcel Energy Center this season and 32-10-2 all-time. He stopped 21 shots to earn his third shutout of the season, robbing Jakub Voracek on a third-period power play, moving from corner to corner with a dive to stop a point-blank shot with his stick.
The Flyers were trying to crack .500 for the first time this season after rebounding from a 1-7-0 start. They're 11-6-2 since a 4-1 victory over the New York Rangers on Oct. 24, but fell to 1-10-1 this season when the opponent scores first.
The Wild's best rush didn't come until 11:06 into the second period when Zach Parise started a 2-on-1 with Koivu. Parise drew Emery to the right corner but instead of passing tried to go five-hole and was turned away at 8:45 on the Wild's 13th shot of the game.
At that point, the Flyers had only six. Coach Craig Beruba pulled Emery with 3:22 left in regulation but the man advantage netted the Flyers only two shots.
NOTES: Flyers C Vincent Lecavalier (back spasms) was a scratch Monday. He entered the game with a team-leading nine goals. . Wild D Mathew Dumba, 19, was one of 25 players invited to Canada's Junior National Team camp on Monday. The only invitee on an NHL roster, Dumba would have to be loaned out by the Wild. That's likely barring an injury on Minnesota's blue line. Camp is scheduled to begin Dec. 12. . Peter Luukko left his job as president and chief operating office of Comcast-Spectacor, which owns the Flyers, on Monday. Luukko will be replaced on an interim basis by Dave Scott, who recently retired as executive vice president and CFO. . The Flyers have killed 14 consecutive power plays.