It was the most saves Allen has made in an NHL regular-season game and the most by a Canadiens goalie in a regular-season game against the Maple Leafs since 1955-56, when shots on goal began being officially tracked.
"In a game like this, against one of the best teams in the League, your goalie has to be your best player, and he was tonight," Montreal coach Martin St. Louis said.
Matthews set his NHL career high with 81 points (34 assists) and tied his NHL career high in goals in his 59th game. Mitchell Marner had two assists for Toronto (40-19-5), which outshot the Canadiens 51-18.
Kallgren made 14 saves in his fourth start in five games for the Maple Leafs, who have lost two of three and host the Florida Panthers on Sunday.
"They always play well and they play hard against us," Matthews said of the Canadiens. "They're fast and skilled, and despite where they are in the standings, this is the NHL and there's good players that are still playing for a purpose, for meaning, whether it's a contract or whatever that might be."
William Nylander tied it 2-2 for Toronto at 7:33 of the third with a power-play goal.
Matthews put the Maple Leafs ahead 1-0 at 36 seconds of the first period with a one-timer from the left face-off dot off a pass from Michael Bunting. He surpassed his point total from 2019-20, when he scored 80 points (47 goals, 33 assists) in 70 games.
"It's great. It means a lot, but in the end it's about winning," Matthews said. "It's about playing a long time this spring and having that success deep into the summer."