Alex Kovalev, Maxim Lapierre and Francis Bouillon also scored for Montreal, which won its fourth straight and moved within five points of first-place Buffalo in the Northeast Division. Sheldon Souray and Sergei Samsonov each had two assists for the Canadiens.
Ales Kotalik and Jaroslav Spacek scored for Buffalo, which has lost consecutive games for the first time this season. Ryan Miller stopped 24 shots.
Montreal has not lost in regulation since Dec. 4.
Kotalik snapped his 13-game drought without a goal, scoring 34 seconds after the opening faceoff. He one-timed a shot from the high slot after Brian Campbell deked around Higgins and delivered a crisp pass.
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 3-2 lead.
Kovalev scored on a shot from the right circle at the 13:01 mark. Saku Koivu collided with Miller, giving enough clearance to provide Kovalev an open net.
Three minutes later, Higgins was stationed along the goal-line during a 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.
Spacek cut the lead to 3-2 with 7:54 remaining in the second period.
Bouillon tipped in a shot with 12:08 left in the game, and Higgins scored his second of the night less than four minutes later to cap the scoring.
Huet has won five of his last six decisions. His only loss during that stretch was in a shootout against Buffalo on Dec. 9.
Notes: 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 was playing in his second game after missing 18 with a sprained ankle. He 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.