Tanguay gained control of the puck during a determined Flames attack and whipped a behind-the-back pass to Iginla, who buried the disc into a half-empty net for the game-winner.
The Blue Jackets, who dropped their fourth game in six contests, got goals from Antoine Vermette and Rick Nash.
Starting netminder Steve Mason was yanked after coughing up two goals on four shots, but Mathieu Garon was saddled with the loss, allowing the game-winner among 21 shots.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys