Price had a season-high 41 saves and Brandon Prust and Lars Eller each had a goal and two assists for the Canadiens as they earned a 4-2 win over the Hurricanes on Thursday.
Eller's goal at 6:09 of the third gave Montreal the lead for good and P.K. Subban added a power-play goal at 7:56 to make it 4-2.
Price, who had given up 12 goals in his previous two starts, was sharp in the first and third periods and faced pressure in the second when the Hurricanes threw 21 shots at him.
"A lot of guys understand that you can't dwell on losses," Price said. "If anybody is struggling, we've got each other's back. I thought we came out strong in the first period and were a little flat in the second, but the most important thing is that we bounced back in the third period."
Carolina's top line of Eric Staal, Alexander Semin and Jiri Tlusty had no success against Price despite combining for 15 shots.
Price stopped Eric Staal's penalty shot with 5:08 left in the second and made a tremendous glove save against Semin also in the second. It was the first time in four games Carolina's top line has failed to pick up a point.
"We couldn't get a bounce or break," Eric Staal said. "The effort was there."
Carolina goalkeeper Justin Peters, playing his second straight game since being called up from Charlotte of the AHL, made 24 saves on 28 shots. Peters has gotten both starts since Cam Ward went out with a knee injury.
Prust opened the scoring at 3:22 of the first and defenceman Josh Georges notched his second goal of the season at 8:19 and Montreal went up 2-0 in the first period.
"They came at us hard in the second," Prust said. "I think we caught ourselves on our heels and didn't respond the right way, but I think we did a good job regrouping during the intermission and had a good third period."
Using an 8-1 shot advantage to start the second period, the Hurricanes rallied as Jordan Staal got his sixth goal of the season with a shot from the right circle at 6:07 to make it 2-1.
Drayson Bowman tied it at 2-2 when he scored his second goal of the season at 10:27 of the second.
NOTES: The Canadiens played their third game of a five-game road trip. ... Carolina recalled F Jeremy Welsh from Charlotte and placed Tim Brent on injured reserve retroactive to Feb. 28. Welsh earned his first NHL point with an assist. ... Montreal coach Michel Therrien was back behind the bench after missing Thursday morning's pregame skate with an illness. ... Montreal D Francis Bouillon played his 700th career game.