His postseason coming-out party came just in time to keep the Lightning alive in their first-round playoff series against the Pittsburgh Penguins.
Stamkos scored his first two NHL playoff goals and the Lightning emphatically avoided elimination with an 8-2 victory over the Penguins on Saturday in Game 5 of the first-round series.
"This kid has figured out what the playoffs are all about," Boucher said. "I knew at some point he would because he's got character. I was just hoping it was this year."
The Penguins, who lead the series 3-2, will get a second chance to advance Monday night at Tampa Bay.
Stamkos' 96 goals the past two seasons led the NHL, but he had only one assist in the first four games of the series. He had three points on Saturday, two days after being held without a shot in the Penguins' 3-2 double-overtime victory in Game 4.
Stamkos, who had 21 goals in his first 22 games this season, had only four goals in his past 26 games, dating to the regular season.
"I'm really happy for Stamkos because the last game I thought he played a great game," Boucher said. "It just didn't pay off for him, and today it paid off. Like I always say, take care of the process and the results will come.
"He was a major warrior in this game."
He wasn't the only one.
Simon Gagne and Pavel Kubina both scored their first two goals of the series, captain Vincent Lecavalier added his second, and Dominic Moore also scored late for the Lightning, who set a franchise record for goals in a road playoff game and handed the Penguins their worst home postseason loss.
Dwayne Roloson made 31 saves, including several impressive stops in the opening minutes when Pittsburgh controlled play.
"[Roloson] was good for the first 17 minutes, and then their team gave them a couple there," Pittsburgh forward Pascal Dupuis said. "Things fell apart after that."
Gagne and Stamkos stunned a Penguins record crowd for an indoor home game with two goals in a span of 46 seconds beginning with 3:03 left in the first.
The road teams have won four consecutive games in the series, and Tampa Bay's victory was the 22nd by a visiting team in 36 NHL playoff games.
"I think me and the rest of the NHL coaches in the playoffs right now are all scratching their heads trying to figure out what's going on with the home teams," Boucher said.
Pittsburgh's Mike Rupp and Chris Conner scored in the third period after Tampa Bay had taken a 7-0 lead, but by then it was obvious the Penguins would fail to become the first Eastern Conference team to advance to the second round.
The Penguins are 0-5 under coach Dan Bylsma when they have the chance to eliminate an opponent at home. The margin of victory was the largest for any playoff game this season.
Counting a 5-1 victory in Game 2, the Lightning have won two straight in Pittsburgh by a combined score of 13-3.
Stamkos' first goal made it 2-0 just after Gagne opened the scoring. Seven minutes into the second period, Stamkos scored his second of the game while the Lightning were on the power play, extending their lead to 5-0.
"I wanted to, obviously, be a part of this team's success in the playoffs and prove to myself and my teammates that I can play in these pressure situations," Stamkos said.
"I just felt each and every game I was getting better and better," he added. "It wasn't showing up on the scoresheet, but I think I noticed it, the coaching staff noticed it, so it's nice to get rewarded, especially in a game of this magnitude."
Stamkos' second goal was the first of three straight man-advantage goals that pushed the Lightning's lead from 4-0 to 7-0.
But the Lightning strikes weren't limited to the power play. They came into the game with only three 5-on-5 goals in the series but had four in the first 26 minutes on Saturday.
Pittsburgh's penalty-killing unit was the best in the NHL during the regular season, but the Lightning went 4-for-7 to make them 8-for-22 for the series.
"There's nothing easy in this league, and we fought," said Martin St. Louis, the Lightning's star through four games who added two assists on Saturday.
"They came out hard, but we stayed composed and [Roloson] made some big saves."
Fourteen of Tampa Bay's 18 skaters had at least a point; eight had at least two. ... Lightning RW Steve Downie and Penguins LW Chris Kunitz each returned to the lineup after serving suspensions in Game 4. Downie had two assists. ... Penguins RW Alex Kovalev assisted on Rupp's goal, his 100th career playoff point. ... The standing-room crowd of 18,535 was the Penguins' 209th consecutive sellout. ... Tampa Bay was outshot 33-25, marking the first time the team with the most shots lost in the series. ... Rupp's goal was his first in the playoffs since scoring the winner in Game 7 of the 2003 Stanley Cup finals for New Jersey.