The latest example played out for all to see.
The centre scored twice at Nashville in Game 7 of the second round in a 5-1 win Thursday night, lifting Winnipeg into the Western Conference finals for the first time.
Behind the scenes, Stastny is also making an impact with intangibles.
"Some of his best performances are things none of us get to see happen inside the dressing room and on the plane and sitting beside the players," Jets general manager Kevin Cheveldayoff said Friday. "We knew we were getting a quality player — obviously, you can see that on the ice. A quality person, we knew that from our due diligence in the past. But what he can bring inside the room … you don’t really appreciate until you have."
The St. Louis Blues valued Stastny, too, but were willing to part ways with him in February because Winnipeg gave up a first-round pick this year, a fourth-round pick in 2020 and a prospect.
"Stastny is a great, veteran player," Vegas coach Gerard Gallant said. "He plays a 200-foot game. He plays on the power play and penalty kill. He was a big pickup for those guys and he’s fitting in well on their team. That’s no surprise to anyone around the game."
With more than 200 goals and 600 assists in Stastny’s career, the Jets invested in this season to make a push in the playoffs and it paid off.
Winnipeg will host the Golden Knights on Saturday night in Game 1 of the Western Conference finals .
"It’s one step closer to where we want to be," Stastny said. "It’s kind of nice that we play really quick, so in one sense we get to enjoy this then forget about it and then focus on Vegas right away."
If a Game 7 proves to be necessary, Vegas will have to keep a close on Stastny because he has a knack for scoring decisive goals.
Just like his father, Hockey Hall of Famer Peter Stastny, who defected from Czechoslovakia with his brother, Anton, in 1980 to play in the NHL.
The 32-year-old Stastny has scored four goals and has eight points in four Game 7s. Just three active players have more points in decisive games: Justin Williams, Patrice Bergeron and Henrik Zetterberg.
When he was seven months old, his father scored in overtime to push the Quebec Nordiques past the rival Montreal Canadiens in division finals of the 1985 playoffs.
"Not that I know my dad’s goals, but I know that one," Stastny said. "Rebound off a draw. He still talks about winning that draw."
No one drew up a conference finals matchup with Vegas and Winnipeg.
And, Stastny is determined to enjoy the ride and help his younger teammates do the same.
"As you get later in your career, you’ve just got to enjoy these moments," he said. "You’re going to have some guys that get nervous out there and that’s fine. It’s our job, older guys, veteran guys, to go out there and try to be loose and try to make everyone comfortable."