It was Gustavsson's second shutout of the season and in his NHL career.
"He's been awesome," Minnesota forward Matt Boldy said. "Nothing but good things to say. He's been standing on top of his head and making saves when he has to, saves he should make and saves he shouldn't make. He's making it easy for us."
Boldy and Joel Eriksson Ek each had a goal and an assist, and Marcus Foligno scored for the Wild (36-21-6), who have won four straight and are 8-0-1 during their point streak.
Minnesota is three points behind the Dallas Stars for first place in the Central Division.
"It's important," Eriksson Ek said. "It's a really important time of year. For us, these games are real big. It's a tight race and we know that. Hopefully we can keep building on this."
Jacob Markstrom made 30 saves for the Flames (27-23-13), who have lost five in a row and are six points behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"I think it was kind of flat on our end from start to finish," Calgary forward Milan Lucic said. "At this point of the year, especially, you should be excited and have a lot of energy to play every single night. That's on us as individuals and that's on us as a team. As players, it's a big part of our preparation. Energy is something we have to create within."