Dillon Dube scored the winner - he was the 14th shooter in the seventh round - to give the Flames their second straight victory.
Ryan Donato and Derek Ryan had both scored in the fourth round.
It was - please excuse the pun - a wild game, with back-and-forth action and the teams trading goals like amped up elementary kids with Pokemon cards.
David Rittich, playing in his 100th game, was especially sharp in overtime and the shootout, denying three one-timers when Minny was given a powerplay early in extra time.
He stopped all seven shooters, of course, in the one-on-one battle at the end, playing aggressive and denying a few of them with well-placed stick checks. He finished the night with 30 saves.
With the aforementioned dads and mentors settled into a box to cheer on their favourite players, it didn't take long to get things going.
Sam Bennett had jump in his step early in the contest, creating the first grade-A scoring chance of the tilt.
The Flames winger drove out of the corner with authority, passing the puck to Ryan in the slot, but Wild sgoaltender Alex Stalock was able to come across and make the stop.
With TJ Brodie in the bin for tripping, the Wild opened the scoring at 5:02, when Kevin Fiala snapped a shot on net that Rittich got a piece of with his glove, but it found its way through him.
The Flames answered back at 9:32 on a powerplay of their own after Minnesota was whistled for too many men.
Mikael Backlund took a sharp angle shot as he skated behind the net and then Rasmus Andersson took a whack at the rebound to the right of the net along the ice, before Wild forward Jordan Greenway tried to clear the puck out of danger and put it off the skate of Milan Lucic and into the cage.
