Smith said he felt a range of emotions unlike anything he'd ever experienced.
"I was down behind the bench with my family," he remembered 20 years later. "It's funny; you don't know how to act. You're wondering, 'Do I go down on the bench? Do I go out on the ice?'
"You're so happy, and you want to go crazy and you've thought about this moment a thousand times. Should I run out on the ice and hug people? What's the right thing to do? It's confusion, euphoria - every emotion you can think of."
He didn't say it, but one of those emotions was probably relief.
The Rangers swept their first two playoff series, then outlasted the New Jersey Devils in seven games to win the Eastern Conference Final and advance to the Cup Final for the first time since 1979. They won three of the first four games against the Canucks, but stumbled at home and lost 6-3 in Game 5, then were defeated 4-1 in Game 6 at Vancouver.
Video: Memories: Rangers win the Stanley Cup after 54 years
Unlike the festive atmosphere before Game 5, there was an air of apprehension before Game 7 - at least among the fans. But the players were much more confident, partly because they were playing at home.
"We played all season to have Game 7 at home," defenseman Jeff Beukeboom said. "We played well enough to earn it. We were definitely prepared, maybe just a little nervous in a positive way.
"We felt confident because we were going to be playing our last game in Madison Square Garden."
The Rangers justified that confidence when defenseman Brian Leetch and forward Adam Graves scored in the first period to put New York ahead 2-0. Canucks forward Trevor Linden cut the Rangers' lead to 2-1 early in the second period, but a power-play goal by center Mark Messier made it 3-1 entering the third.
However, Linden scored again 4:50 into the third period to make it 3-2. To the Rangers and their fans, those last 15 minutes seemed to last an eternity.
"We led 3-2, and it seemed like the time would never end," Smith said. "Those last 15 minutes seemed to last 15 years."
There was good reason for concern. Though the Rangers had won the Presidents' Trophy as the NHL's best regular-season team, they already had lost a couple of last-minute leads during the playoffs -- including their Game 1 defeat to the Canucks.
Vancouver kept the pressure on. Center Nathan LaFayette gave everyone a scare when he hit the post with about five minutes left, and Rangers goaltender Mike Richter often seemed to be in three places at once doing everything possible to keep the puck out.
As if to prove nothing ever came easy, the Rangers survived a last-minute push by the Canucks and looked like they'd won when forward Steve Larmer slung the puck past the blue line and down the left-wing boards. The Rangers and their fans were ready to celebrate - until the whistle blew. Linesman Kevin Collins ruled Larmer had iced the puck, and the Canucks were going to get one more chance.
Leetch and Richter had already started to celebrate.
"I jumped on Mike and gave him a hug," Leetch said. "But then they called icing and put some time back on the clock. When I saw it was 1.1 seconds, though, I wasn't worried. I felt there wasn't enough time for them to do anything, and we had [center] Craig MacTavish taking the draw."
MacTavish was the last of seven former Edmonton Oilers brought in by Smith, who wanted to change the atmosphere in the dressing room after decades without a championship. Smith acquired him prior to the NHL Trade Deadline for just this kind of situation.
Backup goaltender Glenn Healy, watching from the bench, said he knew there would be no heartbreak on this night.
"I've watched [MacTavish] win 90 percent of the draws he took, and I knew he wasn't losing this one," he said. [MacTavish] did what he did best. That's why we went out and got him - to win that draw."
With the clock reset to 1.8 seconds, the Canucks sent their best sharpshooter, Pavel Bure, against MacTavish, who had only one thing on his mind.
"I didn't want Bure to be able to shoot at the net," he said.
MacTavish won the draw, putting the puck into the corner to Richter's right, Larmer pinned his man into the boards as time ran out, and the sweetest sound in franchise history, the final buzzer, signified the wait was over.
For the first time since entering the NHL in 1926, the Rangers lined up on Garden ice to accept the congratulations of the team they had defeated to win the Stanley Cup. The din rose to a roar when NHL Commissioner Gary Bettman spoke the words generations of Rangers fans had been waiting to hear:
"Captain Mark Messier, come get the Stanley Cup."
For decades, the Rangers and their fans had been taunted with chants of "1940." Now they had their own chant: "1994."