Captain Brian Gionta, who was handed the Jacques Beauchamp trophy as the team's unsung hero before the game, scored on a penalty shot 2:04 into overtime to give the Canadiens a 1-0 victory over the New York Rangers on Saturday night.
Price made 41 saves for his sixth shutout of the season, and the Canadiens (46-28-8) ended the campaign with an even 100 points.
"We're definitely proud of our season," said Price. "We put lot of effort in all year long.
"We stayed fairly consistent all year. And now the fun begins."
The Canadiens will face Tampa Bay in the first round of playoff.
They moved one point past the Lightning for second place in the Atlantic Division. However, Tampa Bay can still claim home ice advantage with a victory on their final game Sunday afternoon against Washington.
Price and his teammates expect to watch the game, but won't be upset if the Lightning win or lose.
"I think we're pretty comfortable no matter where we're playing," said Price. "Obviously, we'd like to play here in front of our home crowd, but we're comfortable playing in any rink."
The Rangers (45-32-5) knew before the game they will have home ice for their first round series against the rival Philadelphia Flyers. They rested some veterans, including Martin St. Louis, but still had the better of the play for two periods as they outshot Montreal 39-25 in regulation time and 41-27 overall.
"We didn't mail it in," said New York's Brad Richards. "We could have won the game. But to be honest with you, we're going to turn this page. We're excited to get this week going."
Despite the OT defeat, New York ended the year with an Eastern Conference leading 52 points on the road.
It was a goaltending battle between Price and Cam Talbot, who had shut out Montreal in his first meeting with the Canadiens in November.
"Our goaltender gave us a chance," said Rangers head coach Alain Vigneault. "This game didn't mean anything for us at the end of the day, but we talked about coming here and playing well.
"That's what I thought we did tonight."
The decisive moment came in overtime, as Gionta poked the puck past former Canadien Raphael Diaz at the blue-line, then was tripped by the defencemen as he tried to get free for a breakaway.
Gionta deked to the backhand to beat Talbot on the penalty shot.
"It's something I go to a lot on penalty shots or shootouts," said Gionta. "He's a good young goalie. He holds his ground well. He played well against us."
Coach Michel Therrien was beaming after the game.
"It doesn't happen often that your regular season ends on a penalty shot," he said. "Gionta's our captain, our leader, our unsung hero. It couldn't finish on a better note."
The Canadiens will get back together on Monday to begin preparing for the playoffs, where they hope to redeem themselves after a first-round exit last spring at the hands of the Ottawa Senators.
An area of concern is the power play, which went 0-for-23 over the last eight games.
While Gionta's was their only goal in the final two games, they finished the season on an 11-3-1 run.
The Rangers owned the scoreless opening period, building a 10-2 shot advantage by the 10-minute mark, but couldn't get one past Price.
The Canadiens only woke up somewhat in the second, but Price needed to be even better to keep the Rangers from scoring. He got help from his posts as Derek Dorsett hit one after Price played the puck up the middle, and Diaz hit both posts with a blast off a rush down the right side.
"For the most part, we kept their shots to the outside and didn't allow second and third rebounds," said Price. "We pride ourselves on blocking shots and teams, at this point of the season, are just throwing everything at the net.
"Shots on goal aren't necessarily a reflection of scoring chances."
The Canadiens got two injury scares, as David Desharnais went flying from a Dorsett knee in the first period and Brendan Gallagher came up limping from an open ice collision with Dan Carcillo. Both players finished the game.
"They play hard — I don't think either of those were on purpose," said Gallagher.
In the third, Montreal's Francis Bouillon got two minutes for kneeing Mats Zuccarello, but the player known as The Hobbit was not hurt.
The last time the Rangers lost a game on an overtime penalty shot was Dec. 5, 2002, when the Flyers' Michal Handzus scored in Philadelphia for a 3-2 win.
Notes — Lars Eller missed a third game with a flu for Montreal, while Douglas Murray, Jarred Tinordi and George Parros sat out. Forward Michael Blunden was returned to AHL Hamilton after the game. . . New York rested veterans St. Louis and Ryan McDonagh. Dan Girardi, Chris Kreider and Ryan Haggerty were also out of the lineup.Suggest a correction