It was a frustrating loss for the Wild, who still managed to clinch a playoff spot with Colorado's loss to Vancouver. Kiprusoff continued his dominance of the Wild, making 38 saves in regulation and overtime and then stuffing Pavol Demitra and Brian Rolston in the shootout to deliver a victory for the Flames, who won their fourth in a row.
After getting little help from his offence for the first 65 minutes, Kiprusoff finally got a hand in the shootout.
Tanguay started things by beating Niklas Backstrom high on the stick side, and Iginla scored through the five-hole after Kiprusoff shut down Demitra.
That left it up to Rolston, Minnesota's leading goal scorer, but after a fake shot right in front, Kiprusoff smothered the puck to seal the victory. It was his 21st shutout in a Calgary uniform, breaking Dan Bouchard's franchise record.
The Flames entered the night looking to put some distance between themselves and Colorado for the eighth and final playoff spot in the West, and the players mobbed their goaltender after Rolston's shot to celebrate.
It was a frustrating loss for the Wild, who dominated all game yet couldn't get the puck past Kiprusoff, who entered the night 11-4-3 with a 1.70 goals-against average in his career against the Wild.
The Wild dominated the first period, outshooting Calgary 14-5, but had nothing to show for it after one shot hit the post, another trickled through the crease, and Mark Parrish's goal was disallowed.
The Wild thought they scored when Mikko Koivu blasted a slap shot from just inside the blue-line that Parrish redirected past Kiprusoff. But after an extended review, officials ruled that Parrish played the puck with a high stick and disallowed the goal.
Kiprusoff was equally strong in the second period as the Wild kept the heat on. Midway through, Minnesota held the zone for well over a minute on a single possession that included four slap shots from defenceman Brent Burns, but Kiprusoff turned away every one.
And Minnesota dominated the overtime, keeping the puck in Calgary's zone for most of the five minutes. The session included a golden opportunity for Demitra and Marian Gaborik on a two-on-one. But Gaborik fanned on the pass from Demitra and didn't even get the shot on net.
For all the winning the Wild have been doing lately, they still were tied with Vancouver for first place in the Northwest Division with 97 points when the day began.
Tuesday night's game kicked off a three-game grind for the Wild, who also host the Flames on Thursday before heading to Colorado on Saturday.
At the morning skate, Minnesota coach Jacques Lemaire said how his team plays during this stretch will tell him if the Wild are ready for the playoffs, and the extra intensity that comes with it.
This one certainly had a playoff feel to it, with air-tight checking, little room to work offensively and plenty of pushing and shoving after the whistle.
Notes: Four of the seven games between these teams have gone to overtime. ... One of the Wild's Minnesota-born equipment men had name plates hung in some empty stalls in the Wild dressing room for Herb Brooks and John Mariucci, two Minnesota hockey legends. ... Iginla's shot with 37 seconds left in regulation was his first of the game.