Montreal got off to a quick start, with Begin beating Islanders goalie Rick DiPietro just 56 seconds into the game after Mathieu Dandenault dug the puck out from behind the net.
"Mathieu made a great play," Begin said. "He passed it to (Bryan) Smolinski, and the goalie tried to make a poke check, but the puck rolled back to me so slowly. I had time to let it rip."
The Canadiens didn't look back, scoring three more times in the second period to cruise to victory.
Canadiens left winger and Smithtown native Chris Higgins scored his first road goal of the season in front of 66 friends and family members.
"Good old Long Island came through for me once again," said Higgins. "In all the seasons I've been a pro, I've had more goals on the road than at home, so this is new to me."
The Islanders managed to rally late, starting the third period with a two-man advantage and out-shooting their opponents 20-4 in the final 20 minutes.
Huet was solid throughout, but lost the shutout on a Mike Comrie goal with 3:50 to play.
"A shutout is just a bonus," Huet said. "It's more important to get the win."
DiPietro stopped 29 of 33 Canadiens shots.
Three Stars: 1. Cristobal Huet; 2. Steve Begin; 3. Mathieu Dandenault