After the team's exchanged misses, Tanguay's shot over Jason Bacashihua's glove put Calgary up 1-0. Miikka Kiprusoff denied Doug Weight on a deke giving Iginla the opportunity to clinch it, and the Flames captain came through whipping a shot into the corner over Bacashihua's blocker.
Kristian Huselius had a goal and three assists to pace the offence for Calgary (37-22-10). David Moss, Daymond Langkow, and Dion Phaneuf also scored.
It was an important victory for the Flames who pull within one point of Minnesota, Dallas, and San Jose, who are all tied for fifth place in the Western Conference.
Calgary also pulls to within three points of the Northwest Division-leading Vancouver Canucks.
Lee Stempniak, with a pair, Christian Backman and Peter Cajanek replied for St. Louis (29-29-11).
The Blues outshot the Flames 6-0 in overtime but they could not beat Kiprusoff, who was at his best killing off a Blues power play. Kiprusoff's best stop came with just seconds left as he jabbed out his pad to stop a one-timer from Stempniak.
Tied 2-2 entering the third period, Calgary surged in front to the delight of the sell-out crowd of 19,289 on Phaneuf's power-play goal at 3:16 and Langkow's goal at 6:44.
However, the Blues didn't quit, making it 4-3 just 22 seconds later when Cajanek outbattled Rhett Warrener for a loose puck in the crease, knocking 11th goal of the season. Brad Boyes picked up his third assist of the night, giving the centre eight points during a five-game scoring streak (two goals, six assists).
St. Louis then pulled even at 10:06 on a great individual play by rookie centre David Backes. After crossing the Flames blue-line and drawing two Flame defenders towards him, Backes neatly dished the puck off to Stempniak darting towards the Calgary net. The Blues leading goal scorer make a neat move in-close on Kiprusoff and jammed in his second of the night and 23rd of the season.
Trailing 1-0 after 20 minutes, Moss tied for Calgary at 2:28 converting Matthew Lombardi's centring pass.
Huselius scored an ugly goal to put the Flames in front at 14:01 on his 30th of the season. Huselius took a shot from behind the goal-line that banked off the post, off the back of Bacashihua's leg, and trickled into the net.
Huselius joins Iginla as Calgary's second 30-goal scorer for the season. The Flames have not had two 30-goal scorers since the 1993-94 season when they had four players reach that plateau - Gary Roberts (41), Robert Reichel (40), Theoren Fleury (40), and Joe Nieuwendyk (36).
St. Louis opened the scoring when Backman scored the lone goal of the first period.
Doug Weight spotted the Blues defenceman breaking into the slot from the blue-line and slid him a perfect pass that Backman fired just under the crossbar from 25 feet out.
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.
Notes - Calgary C Craig Conroy sat out with an upper body injury. Conroy was one of the hottest Flames with five points (3 goals, 2 assists) in his last three games... Since taking over as head coach on Dec. 11, Andy Murray has led the Blues to a 22-12-7 record... The Flames have won the last seven meetings between the two teams... Kiprusoff collected his 100th career win as a Calgary Flame... St. Louis is last in the league with 14 power-play goals on the road. No other team has less than 20... Dating back to last season, Bacashihua has gone 15 games - 10 of them starts, since last winning. During that span, he is 0-8-3. His last victory was Apr. 9, 2006.