Price got his second shutout and Andrei Kostitsyn scored twice to lead Montreal to a 5-0 win over Boston on Monday night in the deciding game of their first-round playoff series.
The 20-year-old rookie stopped 25 shots overall, including 11 shots in the opening period. Price had allowed 10 goals overall in a pair of Canadiens losses after he got his first playoff shutout in a 1-0 win in Game 4.
"It was a rough couple of games and we knew it just wasn't going our way," Price said. "I knew it was going to turn around eventually, and tonight it did."
Mike Komisarek opened the scoring 3:31 in amid one of the first of countless roars from the raucous Bell Centre crowd over the course of the evening.
The Canadiens took control of the game in the second, outshooting the Bruins 17-6 while building a three-goal lead on a superb goal by Mark Streit midway through the period and Kostitsyn's second goal of the series at 15:13.
Kostitsyn punctuated the win with his second of the game, a power-play goal with 2:02 remaining in the third. Sergei Kostitsyn scored with 7.3 seconds remaining.
Top-seeded Montreal will face Philadelphia in the second round, if the Flyers win their Eastern Conference quarterfinal against Washington. Otherwise, the Canadiens will face the New York Rangers.
Tim Thomas stopped 30 shots for Boston, which fell short in its bid to overcome both 2-0 and 3-1 series deficits for the first time in team history.
"The character of this team can't be overemphasized, I don't think, for what we battled through all year and even in this seven-game series," Thomas said.
Bruins coach Claude Julien was behind the Canadiens' bench in 2004 when Montreal won three straight to overcome a 3-1 deficit in a first-round win over Boston.
"You've got to give them credit," said Alex Kovalev, who assisted on the Canadiens' first two goals. "They battled back and even down 3-1 and coming back to our building they were able to regroup and get a couple of wins, but the mistakes we made, we didn't compete like we did today. If we had played the way we played tonight I think we could have done it earlier."
Montreal coach Guy Carbonneau moved Kovalev to a line with Saku Koivu and Chris Higgins.
The move allowed rookie Sergei Kostitsyn to play on another line alongside his brother, Andrei, and center Tomas Plekanec as Carbonneau spread out the Canadiens' offense.
"We were trying to give some space to them, to be able to move around and control the puck," Kovalev said.
Komisarek got credit for his first career playoff goal as his point shot struck Bruins center Petteri Nokelainen's stick, causing a deflection that left Thomas no chance to recover and stop.
Streit made it a 2-0 lead 10:45 into the second as he slipped past Bruins captain Zdeno Chara to finish off a sensational passing play. Kovalev passed the puck back to Komisarek in the Canadiens' zone and waited on the right boards at center ice for the return pass.
The high-scoring Russian fed a cross ice pass to Maxim Lapierre as the Canadiens center entered the Bruins zone, and Lapierre dished off to Streit, who pushed the puck past Chara before driving the net to put a backhand between Thomas' pads for his first playoff goal.
"My mouth was wide open seeing that goal," Komisarek said. "The patience and poise that he had with the puck, and to bury it was pretty special."
Andrei and Sergei Kostitsyn combined to increase the lead to three as Andrei beat Thomas at 15:13 for his second of the series, and first since Game 1.
Notes: Veteran Boston RW Glen Murray fell awkwardly into the boards after he was checked by Roman Hamrlik in the first period. A Bruins team spokesman said prior to the second period that Murray suffered a mid-torso injury and that he would not return to the game. ... Carbonneau used the same lineup as he did in Game 6. ... Montreal has never lost a series after leading 3-1.