Tokarski, playing in his 10th NHL game, stopped nine shots each in the first two periods and had 11 saves in the third as Montreal won its second straight game on the heels of a three-game losing streak.
Dale Weise and Brendan Gallagher scored against Sabres starter Jhonas Enroth, who left the game after 36 minutes with what the team said was a lower-body injury.
Nathan Lieuwen, recalled on Sunday from Buffalo's AHL affiliate in Rochester, made his NHL debut in relief of Enroth and stopped 10 shots despite playing for the third straight day.
The Canadiens snapped a two-game road losing streak and earned their fourth straight win over Buffalo. They have points in nine of their last 10 games against the Sabres (6-1-3) and have won all three meetings this season.
Buffalo's losing streak reached six games and its home skid was extended to three. The Sabres have been shut out twice on their losing streak and have just five goals in the six games.
"We need to get out of this funk and keep playing hard," said defenseman Jamie McBain.
Weise's fourth goal of the season got Montreal on the board at the 14:41 mark. The puck, bouncing into the crease after David Desharnais threw a backhand on net, hit off Weise's skate in the crease.
The play was reviewed and upheld as a goal.
Gallagher's 17th of the season was knocked in by Buffalo defenseman Chad Ruhwedel, who was near the crease when Enroth let a rebound get away from him.