They were teammates together in Buffalo when Ramsay, now the Lightning's associate coach, first told Andreychuk about how things aren't always what they seem and that the chance to win hockey's ultimate prize doesn't come around all that often.
"As it turned out, I only got one shot at the Cup," Ramsay said of his 14 years as a player, all with the Buffalo Sabres. "We went to the finals when I was in my fourth year there (1975) and we didn't win, but we were young and we were good and I always thought we would get back there."
It never happened.
"I remember telling a lot of guys back then that if they ever got to that point, to make the most of it, because you never know if you'll have another chance," Ramsay said.
Andreychuk, a 22-year NHL veteran who never played in a Stanley Cup finals before this season, remembered the message.
"We talked about it then, and we talked a lot about it the last couple of days," Andreychuk said. "It was never far from my mind through all the times I thought I would get here and I didn't.
"Rammer always made a point of telling the guys to seize the moment."
Fitting that the two will see their name inscribed on the Cup together.
It was 29 years between opportunities for Ramsay; 22 seasons for Andreychuk.
In the end, Ramsay enjoyed the moment in the quiet of the Tampa Bay coaches' quarters with his wife, Susan, his children, some friends and a six-pack that someone brought to the deepest recesses of the Lightning's inner sanctum.
Andreychuk took the Cup from NHL commissioner Gary Bettman and kissed it.
"You dream about this for a long time obviously," he said. "[It's] taken me awhile to get to this point, and I don't believe you can put into words the things that are going through your mind.
"The years that you got knocked out in the first round ... The years that you didn't make the playoffs, all the players that you have played with and, obviously, my teammates, we battled all year long to get home-ice advantage and it happens to be that we win the Stanley Cup in a seventh game in our own building.
"I will tell you, I can't put it into words the way I feel."
If you ever meet Dave Andreychuk, you will note two things immediately: he's big and he's quiet.
In the early years of his career, his size and scoring touch allowed him to accumulate goals at a Hall of Fame pace, but his silence was misinterpreted as indifference. The knock on Andreychuk was that he had size, natural ability and a gifted scorer's touch, but that he was uninspired by most anything put in front if him.
That could be anything from a bad team meal to the outcome of a game or even an individual battle. Andreychuk just didn't seem to care.
Andreychuk did little to clear up the misconception, so his teammates did.
Mike Ramsey, a teammate of Andreychuk's back then and now an assistant coach with the Minnesota Wild, was among his staunchest defenders.
"He keeps a lot inside," said Ramsey, a former All-Star defenseman with Buffalo, Pittsburgh and Detroit. "Never underestimate Dave's desire to win. He's always had that. Every guy he's ever played with will tell you that."
It's a long list. Andreychuk played with Doug Gilmour and the Toronto Maple Leafs when the Leafs came within one win of advancing to the Cup finals in 1993. He arrived in New Jersey the year after they won their first Cup and left the year before they won their next. He was traded from Boston to Colorado with his friend Ray Bourque in March 2000. Andreychuk left the Avalanche that summer. Bourque won the Cup the next.
He returned to Buffalo during the Dominik Hasek era, but that was after the Sabres' surprise run to the 1999 finals. When it didn't work out there, he signed with Tampa Bay.
Even with the Lightning, arguably the worst team in the NHL when he joined them, there was a decision to be made. Soon after Jay Feaster replaced Rick Dudley as general manager, Andreychuk was offered the chance to be traded to a contender. Feaster said that he didn't want Andreychuk to leave but that he would make the move if Andreychuk wanted to go.
"He didn't want to make the deal, and I agreed with him," Andreychuk said. "I said to him that my job was not done here after one year. I was glad to stick around. I think we did a lot of good things at the end of that [season], my first year here.
"We didn't make the playoffs, but we battled very hard, set ourselves up for the next year.
"Obviously, I'm glad I stuck around."
Unlike his good friend Bourque, Andreychuk didn't cry when Bettman forever put an end to his wait. The nature of his personality wouldn't let it happen. He did, however, seize the moment, hoisting the Cup above his head then kissing it before accepting the ovation from his teammates and the sellout crowd to paraded it around the Forum ice.
"My first thought was not to drop it," Andreychuk said. "Then I wanted to make sure I didn't fall down."
He was joking, but only a little. A lifetime of dreams was suddenly reality, which led to that little happy-feet dance he did before passing the Cup off to teammates.
"You know it runs through [your mind] that this is something that you dream about," he said. "It has taken me awhile to get here. Obviously my teammates deserve a lot of credit for why we're here, but it is a moment that has gone through my head lots of times.
"Finally it happened."
Few failed to recognize the moment.
"I had a chance just to sit with David for a second and congratulate him," Lightning coach John Tortorella said.
"Andy, he keeps to himself, he tries to be unemotional about it, but this guy wanted this bad."
"Dave wanted it, but not just for himself," Ramsay said. "He wanted it for his teammates, too. I think he wanted it for every guy he ever played with."
That would include one former teammate who told him long ago never to give up on a dream -- and who will now join him in getting his name engraved on the Stanley Cup.
Jim Kelley is the NHL writer for ESPN.com.