It happened to the Tampa Bay Lightning four years ago, and the three-time All-Star is determined to not let another opportunity slip away.
After a slow start to the playoffs, the high-scoring team captain helped the speedy Lightning push the New York Rangers to the brink of elimination from the Eastern Conference finals.
Game 6 is Tuesday night at Amalie Arena. A Lightning victory will send Tampa Bay to the Cup finals for the second time in franchise history. And the Rangers are looking to extend the series to a seventh game, which would be played Friday night in New York.
"You kind of have to realize where you are and kind of use that as a little bit of motivation," Stamkos said. "The harsh reality is, some guys in this room may never get the chance to get this far again. Hopefully everybody does, but you never know in this sport."
Stamkos knows first-hand. He and defenceman Victor Hedman are the only players remaining from the Tampa Bay team that came within one victory of playing in the Cup finals in 2011. The Lightning lost Game 7 to Boston 1-0 and didn't win another playoff game until this year.
The two-time Maurice Richard Trophy winner was a young, rising star on that team. Now, he's one of the league's most prolific scorers, leading a club that's flourished in the playoffs even when Stamkos has struggled to score.
After failing to find the back of the net in Tampa Bay's first eight games this post-season, Stamkos has scored in seven of the past 10 to help the Lightning eliminate Montreal in the second round and take a 3-2 series lead over the Rangers.
New York overcame a 3-1 deficit to eliminate the Washington Capitals in the second round. They've been a resilient team in reaching the conference finals three of the past four years, and say they believe they're capable of taking the series back to Madison Square Garden.
"We've obviously been in a few of these situations in the past and are very confident that our group is going to enjoy the opportunity and enjoy the challenge, get ready for it and come up with a good game," Rangers coach Alain Vigneault said.
"We know the situation we're in," New York centre Derek Stepan added. "We have to stay confident."
Stamkos had a goal for the fourth straight game, added an assist on Sunday night, to key Tampa Bay's 2-0 victory in Game 5.
The 25-year-old had 43 goals during the regular season and has been overshadowed for much of the playoff run by the Lightning's young, high-scoring "Triplets" line of Tyler Johnson, Ondrej Palat and Nikita Kucherov, who've combined for 25 of 44 goals in 18 games.
But coach Jon Cooper and Stamkos' teammates insist he's played well throughout, making important contributions in areas other than scoring.
"I think it's funny how it works, because the spotlight is on you so often that everybody just expects greatness all the time. To become great, you do fail sometimes. And he's great. But you don't get there by just success. It's the guys that fight through failure that rise to the top," Cooper said.
"Not that he's failed, but he gets criticized when he doesn't score a goal," Cooper added. "You have to look at what the other team's trying to do, too. It's not like they're putting their eighth pairing defencemen against Stammer. He gets the top guys. ... As this playoff has gone on, Stammer just continues to rise to the occasion."
And that's what the Rangers have to do to keep their season alive.
Henrik Lundqvist rebounded from allowing 12 combined goals in Games 2 and 3 to shut down the Lightning in Game 4. He didn't play poorly in Game 5, and his reputation for excellence in crucial situations is well known.
The Rangers are 3-0 in elimination games this post-season.
"Obviously it's a little different stage than the one we were on before. But a lot of the same things need to be done in order to get ourselves back into it," Stepan said.
"We know how much work it took to get back in the Washington series," Stepan added. "It's going to take just as much work in this series."
Stamkos doesn't expect the Rangers to be an easy out.
"They're a resilient group. We've seen that all series. We've seen that all year. They're the best team in the regular season for a reason," Stamkos said.
"These guys went to the Cup finals last year," the Lightning star added. "How many times have they been down this series and come back? ... We understand the magnitude of the next game, and we're going to get their best game, there is no question about it."Suggest a correction