Brandon Prust broke the deadlock at 2:06 in the final period before Tomas Plekanec and Max Pacioretty also netted shots 28 seconds apart to overwhelm the visiting Hurricanes and give the Canadiens a fourth straight win.
Budaj, filling in for the flu-ridden Carey Price, needed to make just 19 saves to record his first shutout with Montreal.
In Price's absence, Budaj has won a pair of games while fending off 37-of-38 shots.
"It definitely helps my confidence to get two wins and to be able to play well," Budaj said. "Especially when the team in front of me works really hard, I wanted to play really great."
After finishing last in the Eastern Conference a season ago, the red-hot Canadiens (10-4-1) have moved to the top of the Northeast Division in the 48-game lockout-shortened season.
Cam Ward turned back 23 shots for Carolina but folded in the third as the injury-weakened Hurricanes saw their three-game winning run come to an end.
Captain Eric Staal had his 11-game point streak snapped in the defeat for Carolina (8-5-1) as they battled with an ailing lineup.
Forwards Jeff Skinner and Tim Brent along with defensemen Joni Pitkanen and Tim Gleason were all sidelined with injury.
"You're going to have injuries, everyone's going to go through it, and you have to find a way to win," Hurricanes coach Kirk Muller said.
"It was an opportunity for other guys and we just didn't capitalise or get the job done."
- Sports & Recreation
- Ice Hockey
- Brandon Prust
- Carey Price
- Max Pacioretty
- Tomas Plekanec