Montreal forward Ivan Demidov generated multiple power-play chances earlier in the period but could not beat Andersen.
Canadiens head coach Martin St. Louis adjusted his forward lines ahead of the second period to stimulate the offense.
Cole Caufield registered a scoring chance off the rush, while Svechnikov hit the crossbar for the Hurricanes later in the frame.
The Canadiens successfully defended a 1:44 two-man disadvantage later in the second period.
Carolina's Eric Robinson missed an open net from a tight angle shortly after the penalties expired, and Andersen later denied a scoring attempt from Josh Anderson.
The best-of-seven series returns to the Lenovo Center in Raleigh, North Carolina, for Game 5 on Friday.
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If a Game 6 is required, the matchup will return to the Bell Centre in Montreal on Sunday.
