Jordan Kyrou had a goal and an assist, and Ilya Protas had two assists for the Capitals (4-3-0), who had lost two straight, including 4-2 at the Carolina Hurricanes on Tuesday. Charlie Lindgren made 25 saves.
Josh Anderson scored twice, and Lane Hutson had a goal and an assist for the Canadiens (3-3-1), who had won their past two games, including 4-3 in a shootout against the Buffalo Sabres on Tuesday. Alex Newhook assisted on both of Anderson’s goals, and Jakub Dobes made 19 saves.
Justin Holl gave the Capitals a 4-3 lead at 12:29 of the third period when he scored on a wrist shot through traffic from the right point for his second goal in two games.
Alex Ovechkin recorded his 760th career assist on the goal to move within two of tying Nicklas Backstrom (762) for the franchise record.
Tuch made it 5-3 at 17:05, scoring on a spinning shot from the right face-off circle.
Nick Suzuki pulled the Canadiens within 5-4 with a wrist shot from the left circle at 18:21 during a 6-on-4 advantage after Montreal pulled Dobes for the extra attacker during the power play.
Anderson gave the Canadiens a 1-0 lead at 4:29 of the first period. Kyrou turned the puck over in the Capitals' defensive zone and Newhook got to it, skated below the goal line and passed in front to Anderson, who flicked a shot past Lindgren.
Kyrou tied it 1-1 at 7:56 when he took a drop pass from Cole Hutson, deked around Anderson, skated down into the slot and scored on a stick-side wrist shot from the high slot just after a power play ended.
Hutson put the Canadiens up 2-1 after he eluded Capitals forward Ilya Protas at the blue line and scored on a wrist shot from the slot at 11:15.
Ivan Miroshnichenko, making his season debut, tied it 2-2 with a power-play goal at 19:34 when his pass across the crease deflected in off Anderson’s stick.
Tuch gave the Capitals a 3-2 lead at 6:16 of the second period. He picked up the puck off of a deflection, entered the zone on a 2-on-1 rush with Aliaksei Protas and scored a short-handed goal with a wrist shot from the left circle.
Anderson tied it 3-3 with his second goal at 12:58. Newhook stole the puck from Holl along the left boards and passed in front to Anderson for the tip in.
