"It hit me on the inside of the pants, kind of right off the cup there, so it caught me by surprise," Byron said. "It's playoff hockey right now, so sometimes you just got to go to the blue paint, get hit in the leg and get a goal."
WATCH: All Canadiens vs. Canucks highlights
Torrey Mitchell scored 3:57 into the first period and Carey Price made 27 saves for the Canadiens (38-21-8), who lead the Ottawa Senators by six points for first place in the Atlantic Division.
Price has a .964 save percentage while winning his past five starts.
"It's not just me, it's our defensive play in general," Price said. "Our guys did a good job of keeping everything to the outside and battling for the rebounds I left out there."
Canucks forward Michael Chaput tied the game on a deflection with 7:11 left in the third period, and Miller made 36 saves for the Canucks (28-30-8), who fell seven points behind the St. Louis Blues for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"It's almost kind of comical," Miller said of the winning goal, which barely eluded his glove. "It's at your fingertips, it feels like you can do nothing about it. It's right there, but you can't get it. It's a tough feeling."