Budaj was busiest in the second period with eight stops en route to his 10th career whitewash and first since 2010-11, when he was a member of the Colorado Avalanche.
Brandon Prust, Tomas Plekanec and Max Pacioretty each notched a second-period goal for the Habs, who moved into first place in the Northeast Division at 10-4-1.
Cam Ward turned aside 23 shots for the Hurricanes, whose three-game winning streak was snapped.
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