The 20-year-old rookie lost a tooth in a fight-filled, emotional 6-1 win.
The teams combined for 236 penalty minutes and nine players were given a game misconduct.
The Senators have a 2-1 lead in the best-of-seven series and Game 4 is Tuesday night in Ottawa.
Pageau is not likely to forget the score as he was hit in the mouth by Subban on the goal and lost a tooth. Players could be seen looking for the tooth on the ensuing goal celebration.
"I might put it under my pillow and see what happens," Pageau kidded.
The crowd at Scotiabank Place chanted Pageau's name and the Ottawa native says he's hopeful to give them the opportunity to do it again.
"It was good motivation and forced me to push myself to keep going," Pageau said. "They liked my game and I didn't want to disappoint them after that."
The third period started with the Senators leading 2-1.
But after Pageau's second goal of the game and a Kyle Turris score made it 4-1, emotions overflowed and a line brawl broke out at center ice.
Turris' goal, his first of the series, at 7:00 put the game out of reach. On the ensuing faceoff, five different fights broke out.
"I thought we handled ourselves well under the circumstances and the duress we were put under and we defended ourselves," Ottawa coach Paul MacLean said.
The Senators ended up with the man advantage after the brawl and Jakob Silfverberg scored on the power play as he beat Price up high to make it 5-1 only 8 seconds after Turris' goal.
More penalties were taken, and at one point, Ottawa was left with just five players on the bench, while Montreal had six.
Ottawa's veteran forward Daniel Alfredsson finished the game playing defense.
After the game, Montreal coach Michel Therien took exception with MacLean calling a timeout with 17 seconds remaining.
In Therien's opinion MacLean was trying to embarrass and humiliate the Canadiens.
"As far as I'm concerned that was classless," Therien said.
With so few players on his bench and things already out of hand, MacLean felt he had no other option than to call a timeout to get his message to his players.
"I didn't want anyone to get hurt, it was already getting dumb enough as it was," MacLean said. "I have two important players on my team and I still have games to play. We're not giving them a freebie. There's already enough of that."
MacLean went on to say that he was protecting his players and he would do it again.
This is the second time Therien has taken issue with MacLean.
"I don't like when a coach is making comments," Therien said. "I don't like a coach when trying to humiliate our team. I don't like that."
MacLean wasn't impressed by the actions of the Canadiens and is hopeful the league will review certain aspects of the game, including Josh Gorges shooting the puck at Turris at the end of the game.
Pageau completed the hat trick, becoming just the second player in Senators history to get a hat trick in the playoffs with less than two minutes remaining. Alfredsson also did it in 1998.
Less than a month ago, Pageau was playing in the AHL. But his strong play has earned him the confidence of MacLean.
"It was a great night for the kid," MacLean said. "He's come in and played very, very well for us. We're really pleased for him, he's been a good player."
"He played a great game," Alfredsson said. "He had some great shots, picked the corners and it was fun for him."
Alfredsson scored Ottawa's opening goal and Craig Anderson stopped 33 shots.
Price faced 30 shots. Rene Bourque scored for the Canadiens at 14:34 of the first.
The Canadiens had a couple of great chances to tie the game in the second, but came up short.
The Canadiens weren't pleased with their overall effort and know they need a better game plan looking ahead to Game 4 on Tuesday.
"Our problem was we tried to make plays that weren't there," Gorges said. "We weren't in our structure, we weren't in our system and when we're not we're chaotic.
"We knew they were going to come hard, we just didn't play a good fundamental game."
A physical first period ended with the teams tied 1-1.
The Senators made the most of a 28-second two-man advantage as Alfredsson picked up his rebound at his feet and quickly rifled it past the right of Price. It was the Senators' first power-play goal of the series.
Montreal tied the game with a power-play goal as Plekanec found Bourque to create a 2-on-1 break.
Bourque's shot changed speed and seemed to throw off Anderson and he was unable to get over in time and he could only watch as the puck trickle across the goal line.
The Senators are without C Jason Spezza (back, indefinitely). D Eric Gryba served the second and final game of his suspension for his hit on Lars Eller in Game 1. Guillaume Latendresse and Andre Benoit were healthy scratches for the Senators in favor of Cory Conacher and Patrick Wiercioch. With Pacioretty and Gionta back in the lineup, Jeff Halpern and Gabriel Dumont were scratched for the Canadiens.