Marco Rossi had a goal and an assist, Marcus Johansson and Brock Faber scored and Matt Boldy had two assists for the Wild (13-3-4), who had won consecutive games and three of four. Gustavsson made 28 saves.
"I thought we played well tonight," Faber said. "There's positives and negatives from every game and I thought we played well at times and bad at times. That's what a game is. Frustrating, but five out of six [points] on a hard road trip is something we'll take. Going forward, we know what we need to improve on."
Minnesota forward Kirill Kaprizov, who went down after a knee-on-knee collision but remained in the game during a 5-3 win at the Edmonton Oilers on Thursday, did not play due to a lower-body injury. Minnesota coach John Hynes said he is day to day.
"I mean, it was tough adversity on this road trip," Rossi said. "It's going to be three big games for us, and especially with Kirill out ... he's our best player and it's hard when you lose the best player. We know as a team we have to stick together, and everyone had to step up today and I thought we did a pretty good job."
Rooney put Calgary up 1-0 at 15:00 of the first period when he tipped Daniil Miromanov's point shot over Gustavsson's right pad.
Johansson scored 63 seconds later to tie it 1-1 with a one-timer on a feed from Boldy on a 2-on-1 created by Andersson's neutral-zone turnover.
Pospisil gave the Flames a 2-1 lead on the power play at 19:29 of the second when he redirected Nazem Kadri's slap pass past Gustavsson's outstretched right pad.
"It feels great," said Pospisil, who hadn't scored in 19 straight games. "It was kind of frustration the last couple games because I had lots of chances and they didn't end up in the net. It feels great I could help the team that way."
Sharangovich pushed it to 3-1 at 3:53 of the third when he one-timed a pass in the high slot from Connor Zary over Gustavsson's glove on the power play, but Faber trimmed it to 3-2 at 16:01 with a point shot through a screen on the power play.
