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.
Foligno scored his second of the period with 46 seconds left to play in the opening stanza, jamming at the puck in the blue paint through traffic with four Flames around him and knocking it home.
The shots were 14-9 for the Flames in the high-flying first.
The second period featured plenty of chances (22 shots total, 10 for Calgary and 12 for Minny) but no goals.
Early in the third period, it was back to the familiar script.
Michael Stone tied the game up 1:55 in the period, finishing off an around-the-horn, three-way-passing play from Brodie and Ryan, letting a long-distance wrister go that found its way past Stalock through traffic.
The Wild came flying down the ice a few shifts later and put one off the far post, the loud clang a welcome sound to Flames fans.
Gaudreau got spung on a breakaway with 2:52 left and tried to slide the puck five-hole with a backhand but Stalock was able to get his pads shut, although he wasn't sure if he made the stop, looking around in a panic right after.
THEY SAID IT:
DUBE ON WHAT WENT THROUGH HIS HEAD BEFORE HIS S/O TURN:
"At first, I was just taking a deep breath and relaxing. I was really happy that Ritter made that save, it calmed me down a lot going because the game's not over if you miss - that relaxes you a lot."
"It wasn't our best game by any means. I think we were grinding there through the first two. I thought we generated a ton in the third and got rewarded obviously, bit of a lucky bounce on the powerplay but we'll take that. I thought we had a good night. We were committed to winning and guys battled when we needed to to get the extra point."
"That's an important lesson for us to learn. Coming in here we knew there wasn't going to be a lot of room. They do an excellent job in terms of what they do away from the puck and that was the case tonight. And, when you find yourselves in games like that, it's important you do things to keep the puck moving forward and not get yourself in trouble and wait for your chances. I thought we did a good job staying with it and finding a way at the end."
This is the second of three matchups this season between these two clubs. They played the first game of the season-series just two weeks ago where the Wild won 3-0 in Minnesota. They meet again this Thursday. Click here for tickets ... The Flames have a record of 11-12-3 against Western Conference, and are 5-6-2 against the Central Division ... Sean Monahan (397 pts) is just one point away from tying Paul Reinhart (398 pts) for the 14th most points in Flames franchise history ... Flames legends Lanny McDonald and Colin Patterson are on this trip with the team. They talked with Flames TV about what an incredible experience it is for the dads and mentors - and them - to travel for this two-game roadie.
Matthew Tkachuk - Elias Lindholm - Andrew Mangiapane
Johnny Gaudreau - Sean Monahan - Mikael Backlund
Milan Lucic - Derek Ryan - Dillon Dube
Sam Bennett - Mark Jankowski - Tobias Rieder
Mark Giordano - TJ Brodie
Noah Hanifin - Travis Hamonic
Michael Stone - Rasmus Andersson
The Flames finish up this trip in Chicago Tuesday. As mentioned above, they return to the Scotiabank Saddledome on Jan. 9 to host the Wild (click here for tickets). Then, it's a Hockey Night in Canada matchup with the Oilers at the 'Dome on Jan. 11 (click here for tickets).