Cogliano was part of a Ducks team that stunned the Stars in the 2014 playoffs.
Dallas had a 4-2 lead in Game 6 of a first-round playoff series with Anaheim when the Ducks forged a comeback. Anaheim scored twice in the final 2:10 to tie the game, and then Cogliano set up Nick Bonino for the overtime winner 2:47 into overtime
That ended the season for the Stars and sent many a Dallas fan home in heartbreak.
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"We've done it all year. We had games when we clawed back, especially in the third period," Cogliano said. "That's what the playoffs are all about, to keep clawing."
Cogliano has helped the Ducks win five division championships and make the playoffs for six straight seasons. He has been to the Western Conference finals twice with Anaheim in 2015 and 2017.
"He's a definite leader," said Stars GM Jim Nill after acquiring Cogliano. "He has a history of winning everywhere he's been. He's been on winning teams, and he's been a big part of that."