Svechnikov took a pass from Seth Jarvis above the right circle and scored through a screen in front by Sebastian Aho.
Carolina, which also won 3-2 in overtime in Game 2, leads the best-of-7 series 2-1. Game 4 will be here on Wednesday (8 p.m. ET; CBC, TVAS, SN, TNT, truTV, HBO MAX).
Shayne Gostisbehere and Taylor Hall scored for the Hurricanes, who are the No. 1 seed from the Metropolitan Division and Eastern Conference. Frederik Andersen made 10 saves.
Lane Hutson and Mike Matheson scored for the Canadiens, who are the No. 3 seed from the Atlantic Division. Jakub Dobes made 35 saves.
The Hurricanes outshot the Canadiens 38-13, including 15-5 in the first period, when they build a 2-1 lead.
Gostisbehere put Carolina ahead 1-0 at 8:24 of the first. Eric Robinson got the puck during a scrum in the right corner and passed out to Mark Jankowski, whose shot was blocked by Kirby Dach and deflected to Gostisbehere, who then scored off the post past the outstretched blocker of Dobes from the left circle.
Matheson tied it 1-1 at 15:28. He took a pass in the high slot from Ivan Demidov, who was behind the net, and roofed a wrist shot over Andersen’s glove.
Hall put the Hurricanes back in front 2-1 at 16:22, knocking in his own rebound at the left post after his initial tap-in was stopped by the right pad of Dobes. K’Andre Miller started the play by chipping down from the right point to get to a puck dumped into the corner by Jackson Blake.
Lane Hutson tied it 2-2 with a power-play goal at 4:43 of the second period. He worked a continuous give-and-go with Cole Caufield before finishing past the left pad of Andersen on what turned into a 2-on-1 rush.
Noah Dobson appeared to give Montreal a 3-2 lead at 8:28 of the third period, but Carolina successfully challenged that Caufield was offside prior to the goal.
