Daymond Langkow tied it for the Flames with 49 seconds left in regulation and goalie Curtis McElhinney on the bench for an extra attacker. Iginla passed in front to Langkow, who backhanded the puck past Marty Turco.
Dallas drew a delay of game penalty at 1:09 of overtime, and the Flames needed only 16 seconds to capitalize when Iginla -- who also scored in the second period -- fired a shot from the left point that got past a screened Turco.
McElhinney, the backup to Miikka Kiprusoff, made 38 saves and denied a second-period penalty shot in his second start of the season and 21st NHL game.
Turco, back after missing two games due to flu-like symptoms, stopped 19 shots.