Peter Budaj made 19 saves for his second win and first shutout in a Canadiens uniform.
Cam Ward stopped 23 shots for Carolina, who saw their three-game winning streak snapped.
After a fairly uneventful opening 40 minutes, Prust finally broke the scoreless deadlock 2:06 into the third period. Lars Eller led the rush through the neutral zone, before dishing off to Alex Galchenyuk. The rookie evaded Bobby Sanguinetti, before finding Prust driving to the net.
AVALANCHE 6, PREDATORS 5
In Denver, Colorado, Paul Stastny and Jamie McGinn scored 13 seconds apart in the second period as Colorado snapped a nine-game losing streak against Nashville with a win over the Predators.
Shea Weber scored with 1:18 left to make it a one-goal game, the only score of the final period.
Matt Duchene and Aaron Palushaj each had a goal and two assists, while Chuck Kobasew and Tyson Barrie also scored for Colorado, who have been outscored 34-14 by Nashville over the past two seasons.
The Predators pulled to 4-3 on Colin Wilson’s goal, before Stastny and McGinn restored the cushion and forced Nashville coach Barry Trotz to yank Chris Mason, who allowed six goals on 18 shots.
Mike Fisher, Sergei Kostitsyn and Jonathon Blum scored the goals for Nashville.
COYOTES 4, FLAMES 0
In Glendale, Arizona, Mike Smith stopped 30 shots, Keith Yandle scored in the opening minute of the first period and Mikkel Boedker did the same to start the third, lifting Phoenix to their sixth win in eight.
Yandle knocked in a rebound 41 seconds into the game for his fourth point in two games and Boedker scored 30 seconds into the third period by squeezing a puck between Calgary goalie Danny Taylor’s pads in front of a standing-room only crowd.
That was enough for Smith, who was sharp all night for his 22nd career shutout and the third this season. Antoine Vermette and Raffi Torres each added goals in the third period.
Taylor stopped 33 shots in his first NHL start.