Twenty-four seconds into extra time, Jamie Benn knocked the puck into the slot where Seguin was wide open and he put a perfect shot inside the goal post on David Rittich.
Rittich argued he had been interfered with by Benn but after video review the referees allowed the goal.
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Jason Spezza, Benn and Gavin Bayreuther also scored for Dallas (13-10-3), which snaps a four-game winless skid on the road.
Garnet Hathaway, with his first in 16 games, Johnny Gaudreau and Mark Giordano scored for Calgary (14-9-2). The Flames are 4-1-1 in their last six.
Trailing 2-1, the Flames took their first lead midway through the third period on goals 1:10 apart.
Gaudreau tied it, firing a shot top corner for a power-play goal at 9:41. Giordano made it 3-2 with a similar-looking shot from a similar spot, again beating Anton Khudobin with a rising shot over his glove.
But the Stars got it back to even less than three minutes later, Matthew Tkachuk’s clearing attempt went on to the stick of Bayreuther and the rookie defenceman fired his second of the season past Rittich.
Khudobin got the start once again in the absence of Ben Bishop (lower body), who is expected back on Saturday after missing the last five games. The 32-year-old Russian also started in Edmonton on Monday, making 30 stops in a 1-0 overtime loss.
He made 30 saves once again to improve to 5-5-2.
Getting the start over veteran Mike Smith, Rittich finished with 24 saves. He falls to 8-2-1.
The Stars re-took the lead at 18:02 of the second period, needing just 23 seconds to strike on a power play.
TJ Brodie was not able to tie up Benn, stationed in front and he neatly steered in a pass from Seguin.
Dallas struck first, opening the scoring 41 seconds into the game on their first shot.
Spezza slipped into the slot undetected and one-timed a Radek Faksa pass behind Rittich.
Down 1-0 in the first period, Calgary received three consecutive power plays in the first period, but were unable to generate any dangerous chances on goaltender Anton Khudobin.
The Flames tied it shortly after though, with the fourth line coming through. Mark Jankowski set up Hathaway whose one-timer was partially stopped by trickled through Khudobin.