Josh Doan had a goal and an assist, and Noah Ostlund had two assists for the Sabres (26-16-4), who won for the 15th time in their past 17 games. Colten Ellis made 20 saves.
Cole Caufield and Nick Suzuki each had a goal and an assist, and Jacob Fowler made 22 saves for the Canadiens (26-15-7), who have lost three of four (1-2-1). Lane Hutson had two assists.
Thompson’s second goal of the night, and 200th of his NHL career, put Buffalo in front 4-3 at 5:12 of the third period. He took a pass from Doan in the slot and beat Fowler inside the left post.
He completed the hat trick with an empty-net goal at 18:20.
Caufield gave Montreal a 1-0 lead at 3:11 of the first period. He was uncovered in the neutral zone to take a stretch pass from Noah Dobson up to the left circle and scored off the rebound after Ellis stopped his first shot.
Thompson tied it 1-1 on the power play, putting a snap shot through Alexandre Carrier’s legs and beating Fowler short side at 4:05.
Doan’s power-play goal made it 2-1 for Buffalo at 10:30. He took the puck from the corner and roofed it under the bar on the near side.
Ivan Demidov took a feed from Hutson and one-timed it from the right circle on a two-man advantage to tie it 2-2 at 14:20.
Suzuki put the Canadiens ahead 3-2 with another power-play goal at 3:05 of the second period, putting a rebound into an open net after Ellis couldn’t get over in time.
Alex Tuch’s one-timer from the left circle off a pass from Thompson beat Fowler high over his left shoulder to tie it 3-3 at 8:55.
