Seguin's first two goals both tied the game after Florida built leads of 3-0 and 4-3. His two third-period scores against Roberto Luongo were on power plays.
Seguin also assisted on Valeri Nichushkin's score that started the Stars' three-goal surge in the second.
Goals by Rocco Grimaldi, Scottie Upshall and Quinton Howden against Kari Lehtonen built Florida's 3-0 lead in the first 23 minutes.
Lehtonen finished with 13 saves while playing 41 minutes, 49 seconds. After that, Anders Lindback stopped seven shots and allowed Colby Robak's goal that put the Panthers ahead 4-3.
Robak was in the penalty box when Seguin scored the game-winner.
Jason Spezza had three assists and Ales Hemsky added two for Dallas.
The Panthers pulled Luongo in the final minute. He made 23 saves.
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