WATCH: All Kings vs. Canadiens highlights
Montreal will look to set the record on Saturday against the Detroit Red Wings, the team that ended the Canadiens streak in the 1953-54 season.
"It hasn't been perfect," said captain Max Pacioretty, who had two assists. "We're trending upwards after tonight. We have gotten bounces, we've relied on Carey [Price] too much at times, we've had to kill certain penalties that we wish we didn't have to kill, but all things considered we have the right mindset in this room, and when we win a game, no matter what, you kind of look back on that game and see there's not a turning point, but there's a reason for the guys to stand up and feel good about themselves because we play for one another."
Price set a Canadiens record with his ninth win in as many starts this season. The former record of eight was set by Charlie Hodge in the 1960-61 season, according to the Elias Sports Bureau.
Price's 12-game winning streak is the longest by an NHL goalie since Jonas Hiller won 14 consecutive games for the Anaheim Ducks from Dec. 6, 2013 to Jan. 12, 2014.
Montreal led 3-0 when Tyler Toffoli's power-play goal ended Price's shutout bid at 11:57 of the third period.