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.
The Sabres are 4-for-10 on the man-advantage in their past two games after a 1-for-21 slump in their previous 10 games.
“Efficiency’s pretty hot,” Sabres forward Alex Tuch said. “Our power play was buzzing. A lot of opportunities like that, a couple more tonight. ‘Doaner,’ heck of a play. 'Tommer,' great shot. It was everybody rolling and they were feeling it and really good, too.”
Ivan Demidov took a feed from Hutson and one-timed it from the right circle on a 5-on-3 power play 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.
Montreal entered the game 3-for-30 on the power play in its previous 10 games.
“We haven’t been great lately, just trying to get that going again to help our team win,” Suzuki said. “We scored a couple (but) just didn’t do enough 5-on-5 and on the (penalty) kill.”
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.
NOTES: Hutson had his 25th multiassist game in his 132nd career game, second fastest by a defenseman in NHL history behind Mark Howe (119 games). He also became the second fastest defenseman to 100 assists after Sergei Zubov (127 games). … Demidov has 40 points (11 goals, 29 assists) in 48 games to tie Chris Chelios for fifth fewest games to reach the mark by a rookie in Canadiens history. … Thompson’s hat trick was the ninth of his NHL career, tying Dave Andreychuk for fifth most in Sabres history. … Thompson tied Patrick Kane for second most hat tricks among active American players, trailing only Auston Matthews (14). … Buffalo won its eighth game since the NHL’s holiday break, second most among all teams behind the Tampa Bay Lightning (nine). … Before the game, the Sabres honored their 2005-06 team as part of Reunion Night, with 18 players getting introduced at center ice.