Cole Caufield had a goal and an assist, Lane Hutson had two assists, and Jakub Dobes made 26 saves for Montreal, the No. 3 seed in the Atlantic Division.
Tage Thompson and Rasmus Dahlin each had a goal and an assist, and Alex Lyon made 31 saves for Buffalo, the No. 1 seed in the Atlantic.
Montreal leads the best-of-7 series 2-1. Game 4 is back at Bell Centre on Tuesday (7 p.m. ET; ESPN, SN, CBC, TVAS).
Thompson put the Sabres up 1-0 when he scored 53 seconds into the first period. Dahlin’s shot from the point caromed off the end boards, hitting Canadiens defenseman Alexandre Carrier’s right leg and changing direction before Thompson put away the rebound in front.
Newhook tied it at 1-1 at 15:31 with his first goal of the game. After battling with Buffalo defenseman Bowen Byram for possession behind the net, Newhook came out front to put away the rebound of Jake Evans’ shot, which hit off the stick of Sabres defenseman Conor Timmins and past Lyon.
Caufield put Montreal up 2-1 with a power-play goal at 6:05 of the second period. After his tap-in opportunity went wide of the left post in the opening minute of the period, Caufield made no mistake on another chance at an open net when Hutson set him up in front for the snap shot past Lyon glove side.
Zachary Bolduc made it 3-1 at 10:43 when he drove in from the right side and one-timed a pass from Joe Veleno to snap a shot past Lyon stick side.
Juraj Slafkovsky pushed it to 4-1 at 12:17. He scored Montreal’s second power-play goal of the game when he set up in front and deflected Hutson’s shot past Lyon.
Dahlin cut it to 4-2 at 14:46 with a power-play goal. He used teammate Zach Benson, as well as Montreal’s Mike Matheson and Newhook, as a screen to put a wrist shot past Dobes stick side that bounced off the post and in.
Kirby Dach made it 5-2 at 8:46 of the third period when Alexandre Texier’s shot hit the left goal post, with Lyon moving to make the save and leaving his backside open for Dach’s finish in front.
Newhook, who scored twice in Montreal’s 5-1 Game 2 win at KeyBank Center on Friday, was awarded a goal by the referee for the 6-2 final at 15:14 when he was hooked by Dahlin and hit the post after driving in on an empty net with Lyon pulled for the extra skater.