The Blues rallied from a two-goal third period deficit and nearly win it in overtime before the Flames, pulled it out in the tiebreaker.
"You don't want to win a game 5-4 in a shootout, that's for sure, but we'll take the points right now and run," Tanguay said.
After the team's exchanged misses, Tanguay's shot over Jason Bacashihua's glove gave Calgary the edge. Miikka Kiprusoff denied Doug Weight on a deke, giving Iginla the opportunity to clinch it. He whipped a shot into the corner over Bacashihua's blocker.
Kristian Huselius had a goal and three assists for Calgary. David Moss, Daymond Langkow, and Dion Phaneuf also scored for the eighth-place Flames, who pulled within one point of Minnesota, Dallas, and San Jose in the Western Conference playoff race.
Calgary also climbed within three points of the Northwest Division-leading Vancouver Canucks.
"You've got to give credit to [the Blues], they never stopped working hard and they came back and came back after us," Huselius said. "We thought it was over when we got the 4-2 lead."
The Blues outshot the Flames 6-0 in overtime but couldn't beat Kiprusoff, who was at his best when killing a power play.
Kiprusoff's best stop came in the waning seconds when he jabbed out his pad to stop Stempniak's one-timer.
"We had great chances but Kiprusoff made an unbelievable save," Weight said. "Kiprusoff's a great goalie and he deserves a lot of the credit."
The Blues' refusal to quit despite being out of the playoff race is indicative of how the team's played since Andy Murray became coach on Dec. 11. Since then, the Blues are 22-12-7.
"We came back a couple times in the toughest building in the league to play in," Weight said. "Since Andy has taken over, this team is top five in the league. We believe now that every game we go out, we're going to be in it until the end and it makes for a great feeling coming to the rink these days."
The Flames took a 4-2 lead in the third period on Phaneuf's power-play goal at 3:16 and Langkow's goal at 6:44. But the Blues responded, making it 4-3 just 22 seconds later when Cajanek scored his 11th goal. Brad Boyes earned his third assist of the night, giving the center eight points during a five-game scoring streak.
St. Louis pulled even at 10:06 on a great play by rookie David Backes. After crossing the Flames blue line and drawing two defenders toward him, Backes neatly dished the puck off to Stempniak darting toward the Calgary net. The Blues' leading goal scorer jammed in his second of the night and 23rd of the season.
Moss lifted Calgary into a 1-1 tie at 2:28 of the second period.
Bacashihua made his first start since Dec. 13 for St. Louis and made some sensational saves in finishing the night with 30 saves.
Kiprusoff finished with 29 stops.
Calgary C Craig Conroy sat out with an upper body injury. ... The Flames have won the last seven meetings between the teams. ... Kiprusoff earned his 100th victory with the Flames. ... St. Louis is last in the NHL with 14 power-play goals on the road. No other team has fewer than 20. ... Dating to last season, Bacashihua has gone 15 games -- 10 starts -- since his last victory on April 9, 2006. He is 0-8-3 in that span.