Price made 25 saves for his first shutout of the season and P.K. Subban had a goal and an assist to lead the Canadiens to a 4-0 win over Carolina on Wednesday.
Price, who earned a secondary assist on Michael Cammalleri's goal 7:15 in, recorded his first regular-season shutout since March 12.
"I just needed to get a fight or something, a goal would have been nice, but I'll take what I got," said Price, who posted his 13th NHL shutout.
"It was a solid effort all the way through," captain Brian Gionta said. "We were doing the right things, and obviously Pricey made some huge saves."
Cam Ward stopped 32 shots for Carolina, which lost 5-3 to Philadelphia on Monday.
"We're clearly struggling and I think we've felt that tension for a while," coach Paul Maurice said.
The Hurricanes are 3-8-2 in their last 13 games.
"No question there's concern," Carolina captain Eric Staal said. "Obviously, if we keep losing we're not going to be in the mix for the playoffs. So we've got to figure this out and get back to winning some games because if you keep losing, you're going to be out of the picture before you know it and the season's going to be wasted."
Frederic St. Denis made his NHL debut for the Canadiens, who had three rookie defensemen in the lineup.
With Hal Gill sidelined by illness for a second straight game, and Jaroslav Spacek out because of an injury sustained Monday in the Canadiens' shootout loss to Buffalo, Josh Gorges was the only one of Montreal's six defensemen who has played more than 100 NHL games.
"It's like if you're sick before a game, you always find that when you're not 100 percent you always play your best games," said Subban, a sophomore who was second in experience to Gorges with 97 games. "As a group, when we made mistakes we worked hard to make up for it."
Cammalleri, who missed Monday's game because of an undisclosed lower body injury, opened the scoring with his fourth goal.
Plekanec earned his second straight assist with a pass to former Carolina forward Erik Cole to begin the play that led to Weber's power-play goal that made it 2-0 at 15:16.
Cole, who left the Hurricanes to sign a four-year, $18 million contract with Montreal in July, fed the puck through a seam to Weber. He beat Ward with a shot from the left side.
Subban increased the lead to 3-0 when he scored from the slot for his first goal of the season. Subban celebrated by skating to the left corner and jumping up against the glass with his hip.
Moen made it 4-0 with 38.2 seconds left in the second period. He scored from behind the net, banking a backhanded shot from the end boards in off the bottom of Ward's pads.
- Hurricanes D Joni Pitkanen missed his third straight game because of an undisclosed lower body injury.
- St. Denis was recalled from Hamilton of the AHL on Tuesday. Raphael Diaz and Alexei Emelin were the other rookie defensemen in the Canadiens' lineup.
- Gorges has played 382 NHL regular-season games with Montreal and San Jose. Weber has played 67 games.
- Price recorded his third playoff shutout in Montreal's 2-0 win over Boston on April 14 in the opening game of the Canadiens' first-round loss to the Bruins.