Higgins scored twice and Huet made 42 saves, leading the surging Canadiens to a 5-2 victory and cutting Buffalo's lead in the Northeast Division to five points.
"If you were to ask us a month and a half ago if this was possible, everybody would have laughed," Montreal coach Guy Carbonneau said. "One game can change a lot of things. We wanted to win this game and put pressure on them."
"It's always a four-point game against a division opponent," said Huet, who was won five of his last six decisions. "We look a little more at the top. But we try to focus on our business and catch them."
"Trying not to lose two in a row is an extremely tough task," said Sabres coach Lindy Ruff, whose team has a two-game road trip before the Christmas break. "It's going to be interesting how we react."
Kotalik scored 34 seconds after the opening faceoff, snapping his 13-game drought without a goal. He one-timed a shot from the high slot after Brian Campbell deked around Higgins and delivered a crisp pass.
"I liked the start," Ruff said. "I thought we could have taken better advantage of it. We'll give them credit, but our penalty kill got a little disjointed."
The early lead was erased quickly later in the period, however, as Montreal scored three goals in 4:32 -- two on the power play -- to take a 3-1 lead.
Kovalev scored on a shot from the right circle at the 13:01 mark. Saku Koivu collided with Miller during a power play, giving enough clearance to provide Kovalev an open net.
Three minutes later, Higgins was stationed along the goal line during another power play and steered in Sergei Samsonov's shot.
Just 81 seconds elapsed before Lapierre made it 3-1, stuffing in a rebound between Miller's legs. Lapierre, who has played four games with Montreal this season, extended his goal-scoring streak to three and has a point in every contest.
"We battled back pretty good," said Higgins, who was playing in his second game after missing 18 with a sprained ankle. "We still gave up a lot of shots, but our power play did the job and we got some key saves down the stretch."
Spacek cut the lead to 3-2 with 7:54 remaining in the second period.
Huet, whose only loss in the last six games came in a shootout against Buffalo on Dec. 9, stopped 17 shots in the third period, blanking Buffalo while his team got two more goals to cushion the lead.
Bouillon scored on a shot from the point with 12:08 left in the game, and Higgins netted his second of the night less than four minutes later to cap the scoring.
"We didn't meet one of our goals of not losing twice," Miller said. "It's not the end of the world, but we should feel a little ticked off."
Buffalo F Clarke MacArthur made his NHL debut. He led Rochester (AHL) in scoring with 12 goals and 22 assists for 34 points. ... Kotalik's goal was the second time this season the Sabres scored in the game's opening minute. Henrik Tallinder scored 33 seconds after the opening faceoff at Ottawa on Oct. 7. It was the fastest goal allowed by Montreal this season. ... Higgins scored two goals for the fifth time in his career. ... The Canadiens, boasting the league's most effective power play, went 2-for-4 with the man advantage. Buffalo was 0-for-4 and is 5-of-60 in its last 11 games.