Kirill Kaprizov had a goal and an assist, Danila Yurov, Vinnie Hinostroza and Matt Boldy each scored for the Wild (31-14-10), who have won two in a row and are 5-1-1 in their past seven games.
Morgan Frost scored and Devin Cooley made 20 saves for the Flames (21-26-6), who have lost five straight (0-3-2).
Despite allowing two goals in the first period, Calgary outshot Minnesota 13-3.
Yurov made it 1-0 at 2:43 of the first period, snapping the puck off a backhanded pass from Vladimir Tarasenko down low.
Hinostroza added another to make it 2-0 Wild at 10:37. Jake Middleton sprung Hinostroza for a partial breakaway with a stretch pass, allowing him to get a wrist shot over Cooley’s right shoulder.
After a scoreless second period, Frost cut the deficit 2-1 at 5:49 of the third period. He put a wrist shot past Gustavsson to finish a 2-on-1 rush with Jonathan Huberdeau.
Boldy extended the lead 3-1 at 17:17 on the power play, with Kaprizov feeding him in the slot for the tip-in.
Kaprizov scored into the empty net just 28 seconds later for the 4-1 final at 17:45.