Kessler first scored during a 5-on-3 power play 3:24 into the game and Tom Sestito doubled the Canucks' advantage later in the first period.
But that deadlock lasted less than a minute as Kesler notched his second goal, putting Vancouver ahead to stay.
Eddie Lack stopped 29-of-31 shots for the Canucks, who were coming off a 5-2 loss to the New York Rangers Friday.
Cam Ward made 27 saves for Carolina.
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