Gelinas got to a loose rebound in the crease and knocked it past Detroit goaltender Curtis Joseph to eliminate the top-seeded Red Wings.
"It was a great team game," Gelinas said. "I'm just happy to be in the right place.
"They had more skill, but we worked extremely hard and it paid off."
His heroics against Detroit came two weeks after he'd done the same thing to the Vancouver Canucks in the first round, though that goal came in Game 7 and took 1:25 of overtime.
His first NHL overtime goal, on May 28, 2002, gave the Carolina Hurricanes a 2-1 victory at the Toronto Maple Leafs in Game 6 of the Eastern Conference Final, moving them into the Stanley Cup Final for the first time since they entered the NHL as the Hartford Whalers in 1979.
That was his third trip to the Final; he played on the Edmonton Oilers' Cup-winning team in 1990, capping his first full season in the League, and was a member of the 1994 Canucks, who lost to the New York Rangers in seven games.
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Gelinas added to his legend in the 2004 Western Conference Final against the San Jose Sharks, when his second-period goal in Game 6 was the series winner for the Flames, though they didn't have to go to overtime in the 3-1 win.
"You just have to get there," Gelinas, now an assistant coach with the Flames, told the Calgary Herald in 2014. "But I had that burning desire. I mean, I bleed red for this city. As an older guy, I knew that someone has to take charge, someone has to lead the way. [Jarome Iginla] did, because he had more skill. But in a different way, I wanted to show what I was capable of doing."
The 2004 series winners, each of which eliminated a division champion, were part of Gelinas' NHL career-best postseason; he finished with 15 points (eight goals, seven assists) in 26 games.
"He obviously got the important goals," defenseman Andrew Ference told the Herald, "but he showed, especially the young guys on the team, that those goals aren't just fortunate luck. That comes out of years and years of hard work, conditioning, being a real pro. He was the epitome of what you should be as a professional."