The Kings (16-4-3), who eclipsed the mark of 10 straight road wins set by the Buffalo Sabres in 2006-07, are one road win away from matching the NHL record of 12 consecutive road victories at any point during the season.
Drew Doughty had a goal and an assist and Trevor Moore also scored for Los Angeles. Anze Kopitar had three assists and Talbot made 24 saves.
Montreal was shut out by Los Angeles for the second time this season. The Kings earned a 4-0 win in Los Angeles on Nov. 25.
Samuel Montembeault stopped 38 shots and became the first Canadiens goalie to start consecutive games since Jake Allen on Oct. 21 and 23.
Byfield continued his breakout season after a slow start to his career. The second overall pick in 2020 has eight goals and 13 assists through 23 games this season.
The Kings went 1 for 1 on the power play, while the Canadiens failed to score on three man-advantage situations.
Doughty opened the scoring at 8:13 of the first period when he controlled the puck on a broken play in the offensive zone and slid a shot under Montembeault for his seventh goal of the season.
The Canadiens outshot the Kings 13-11 in the opening period and had a number of scoring chances.
On the same power play, Sean Monahan hit the post with a shot and Juraj Slafkovsky hit the side of the cage from a wide angle on an open net.
Byfield scored his first of the game at 17:46 by cutting hard to the net, fending off Canadiens defenseman Kaiden Guhle and tucking the puck past Montembeault’s left pad.
Byfield converted on the Kings’ first chance on the man advantage at 18:15 with a shot into an open cage from the side of the net after Kopitar tipped a pass from the point onto his stick.
Moore added to a goal 7:58 into the third period with a breakaway goal after Canadiens defenseman Justin Barron tripped on a linesman.
The Kings outshot the Canadiens 31-11 in the final two periods.
Before the game, the Canadiens held a ceremony for recent Hockey Hall of Fame inductee Caroline Ouellette.
The Montreal-born Ouellette is one of three women’s hockey players to capture four Olympic gold medals (2002, 2006, 2010, 2014). She also won six world championships for Canada.
Up next for the Kings: At the New York Islanders on Saturday.