Keefe said Tavares was conscious, communicating well and that tests so far have come back clear, but that the center will remain in the hospital overnight for further tests.
Teams that win Game 1 are 490-222 (68.8 percent) winning a best-of-7 NHL playoff series, including 7-1 in the first round last season.
Game 2 is here Saturday (7 p.m. ET; CNBC, CBC, SN, TVAS).
Montreal is facing Toronto in a playoff series for the first time since 1979; the Canadiens have won nine in a row against the Maple Leafs in the postseason.
Byron shielded Maple Leafs defenseman Rasmus Sandin from the puck then shot it past Campbell, who attempted a poke check, to give the Canadiens the lead at 12:44 of the third.
"He's a feisty player," Price said. "He battles in practice. He's always doing that in practice. He's a finisher and I'm happy for him."
Price made a blocker save on Mitchell Marner, who one-timed a pass from Nylander on a 2-on-1, at 9:38 of the third to keep the game tied.
"I was just trying to read and react and cover the low, as one wise man once told me," Price said.
Toronto was 0-for-4 on the power play, including an opportunity at 16:42 of the third period when Phillip Danault took a minor penalty for tripping.
The Maple Leafs were 5-for-5 on the penalty kill.
"The penalties, let's be honest, it's playoff time, you can't just give teams life by giving them power plays," Toronto forward Nick Foligno said. "It was a really choppy game, nobody gets a feel for it and it takes away from what we are good at, which is being a 5-on-5 team and being dangerous holding on to pucks. It seemed like we were parading to the box. We have to find a way to get our offensive flow going."