The Canadiens lead the series 3-2. Game 6 is at Bell Centre in Montreal on Saturday (8 p.m. ET; ABC, SN, CBC, TVAS).
Ivan Demidov scored his first career Stanley Cup Playoff goal and had an assist, and Juraj Slafkovsky had three assists for the Montreal, which is the No. 3 seed in the Atlantic Division. Phillip Danault and Lane Hutson each had two assists, and Jakub Dobes made 32 saves.
Jason Zucker, Josh Doan and Konsta Helenius scored for Buffalo, the No. 1 seed in the Atlantic.
Ukko-Pekka Luukkonen allowed five goals on 23 shots before being replaced at the start of the third period by Alex Lyon, who made two saves.
The teams combined for five goals in the opening 10:15.
Zucker gave the Sabres a 1-0 lead at 2:00 of the first period. Jack Quinn put a wrist shot towards net from above the left face-off circle, and the puck deflected off Zucker's right skate and then off Montreal defenseman Mike Matheson in front before going into the net. It was Zucker's first playoff goal since April 21, 2024, when he was a member of the Nashville Predators.
Cole Caufield tied it 1-1 at 6:31, redirecting Suzuki's pass into an open net following a Buffalo turnover in the defensive zone.
Doan put the Sabres up 2-1 at 7:45 when he finished a feed from Owen Power with a one-timer from above the left circle.
Alexandre Texier evened the score 2-2 just nine seconds later at 7:54 after Alexandre Carrier's wrist shot from the blue line deflected in off his left skate as he battled for position in front of the net.
Helenius gave Buffalo a 3-2 lead with his first playoff goal at 10:15, skating into the offensive zone and putting a wrist shot through the five-hole from the edge of the right circle. It was also the first point of the postseason for Helenius, who played his first playoff game on May 12.
The Canadiens scored three goals in the second period to take a two-goal lead.
Josh Anderson tied it 3-3 at 8:01 of the second period when he finished a backdoor pass from Hutson.
Jake Evans put Montreal ahead 4-3 at 16:15. Demidov's initial wrist shot from the right circle squeaked through Luukkonen and Evans poked the loose puck over the goal line as he crashed the net.
Suzuki scored a power-play goal to make it 5-3 at 17:33, snapping the puck under the right pad of Luukkonen from the right circle off a Slafkovsky pass.
Demidov pushed the lead to 6-3 at 3:32 of the third period when he beat Lyon to the glove side with a wrist shot from the high slot while on the power play.