Jake Muzzin scored twice in 5:02 in the third period, and Jack Campbell made 26 saves for the Maple Leafs, the No. 1 seed in the North. They lead the series and are trying to advance to the second round of the Stanley Cup Playoffs for the first time since 2004.
"It's tough to close a team out," Campbell said. "They came out hard. I thought we played well enough to win the game; I just can't give up three in regulation. I have to be better, and I will be. I just have to make the save on that 2-on-0. I was a little aggressive, so I'll learn from it."
Game 6 will be played at Montreal on Saturday (7:30 p.m. ET; NBCSN, CBC, SN, TVAS). The Canadiens are expecting to have about 2,500 fans in attendance, which would be the first NHL game in Canada with fans since March 11, 2020.
"I think to be honest, the fans will deserve that game big time," Montreal forward Phillip Danault said. "It's going to be crazy there, it's going to be awesome and I can't wait to be in front of our fans.
"We've been waiting for that all year and here we are, Game 6 against Toronto Saturday night at home. It can't get any better than that."
The Maple Leafs trailed 3-0 but started to rally at 6:32 of the second period when Zach Hyman scored from the slot after Mitchell Marner played it in front from the side of the net with Price out of position to make it 3-1.
Muzzin cut it to 3-2 with a shot from the point at 6:52 of the third, then tied it at 11:54 when he deflected a shot from Galchenyuk in the slot to make it 3-3.
Toronto outshot Montreal 16-6 in the third period.
"I think everybody knew what the overall message should have been (after the third)," Price said. "I don't think anybody needed to say anything. Our coach came in and gave us a few words, but you look around the room and everybody knew what was at stake."