Iginla won it with a slapshot less than two minutes into the extra session.
Calgary's Daymond Langkow had tied the score in the final minute of regulation. Iginla, who assisted on the Langkow score, got his other goal in the second period.
Curtis McElhinney stopped 38 shots for the Flames.
Loui Eriksson and James Neal registered the Stars' goals.
Marty Turco -- who had sat out two games with flu-like symptoms -- stopped 20 for Dallas, which has lost three straight games.
Copyright 2009 by United Press International.