Pacioretty added an assist and Brandon Prust also scored for Montreal in the third.
Peter Budaj made 19 saves for his second win of the season and his first shutout in a Canadiens uniform.
Cam Ward stopped 23 shots for Carolina, which saw its three-game winning streak snapped.
The Canadiens had the better opportunities through a fairly uneventful opening 40 minutes, forcing Ward to make big stops on David Desharnais in close and Plekanec on a 2-on-1 with P.K. Subban coming out of the penalty box.
Prust finally broke the scoreless deadlock 2:06 into the third period. Lars Eller led the rush through the neutral zone before dishing off to Alex Galchenyuk. The Canadiens' rookie evaded Hurricanes defenseman Bobby Sanguinetti with some slick moves before finding Prust driving to the net.
The Canadiens doubled their lead when Plekanec took a pass from Pacioretty and tossed a shot from inside the left circle at 12:03. The puck bounced on to Ward's back and into the net, giving the Canadiens' center his eighth goal of the year.
Pacioretty finally scored his first of the season at 12:21 when his innocent-looking shot from the red line trickled past Ward.
NOTES: Canadiens goaltender Carey Price was back in the lineup, dressed as