Max Domi gave the Canadiens a 1-0 lead at 6:05 of the first period.
Shea Weber made it 2-0 with a slap shot from above the right face-off circle off a pass from Kenny Agostino from below the goal line at 7:36 of the first.
It was the 10th straight game Chicago allowed the first goal and ninth in the past 10 they allowed at least two goals in the first period.
"It's just, like, we talk about it, and it's very, very frustrating, especially when it keeps happening," Kane said. "I'm sure we'll keep addressing it, keep trying to figure it out, keep trying to go [new] ways about it, maybe switch things up, I don't know. It's frustrating that it keeps happening."
Kane scored on the power play to make it 2-1 with 59 seconds remaining in the first.
He tied the game 2-2 at 12:55 of the second period on a one-timer from the right circle off a Dominik Kahun cross-ice pass.
"I picked up the pass a little late and I didn't get the push that I wanted, so I reached for it," Price said. "I don't know if it was the ice conditions or what, but I don't think he got all of it, just found a way to float it over my head."
Chicago defenseman Connor Murphy had four shots on goal and three hits in 16:46 in his season debut. He missed the first 31 games with a back injury.
"Physically, I felt good," Murphy said. "It was nice to get into a normal rhythm at the start of the game. Yeah, just getting into the flow of it was good. It was nice to have a home game. I felt like the guys were skating pretty well tonight and didn't have too much time defending, which is always nice to play a little more offense. So that part of it was good."
