The Montreal captain pushed his season total to 91 points (26 goals, 65 assists), setting an NHL career high.
Cole Caufield scored his 46th goal and had an assist, Lane Hutson had two assists and Jakub Dobes made 34 saves for the Canadiens (42-21-10), who have won six of seven.
Andrei Svechnikov scored for the Hurricanes (46-21-6), who have lost two of their past three games. Frederik Andersen made 15 saves.
Carolina took a 1-0 lead with a power-play goal at 8:37 of the first period. Svechnikov took a pass from Seth Jarvis in the right circle and one-timed a shot under the crossbar.
Montreal scored off the rush to tie the game 1-1 at 6:18 of the second period. Caufield took a stretch pass from Hutson before pulling up in the left circle and feeding Suzuki, who scored driving the net.
The Canadiens scored on a similar play to make it 2-1 at 17:32. Suzuki took a pass from Hutson through the neutral zone and passed to Caufield for a snap shot that beat Andersen blocker-side.
Suzuki made it 3-1 with a power-play goal at 19:54. Andersen made a sprawling right-pad save on Suzuki at the top the crease, but the Montreal forward scored on the rebound.
