Price, in his fifth NHL season, has 13 shutouts in his career. Eight of them came last season.
After losing seven of their first eight games this season, the Canadiens have won seven out of 10.
Mike Cammalleri opened the scoring with a slap shot that beat Cam Ward 7:15 into the contest and Yannick Weber produced a power-play goal with 4:44 left in the first period.
P.K. Subban and Travis Moel tallied in the second stanza.
Ward gave up all four goals on 33 shots. Carolina has dropped two in a row.