Vancouver finished off a six-game road trip with its third straight loss. Roberto Luongo made 29 saves.
Dorsett gave Columbus a 3-1 lead at 14:23 of the second with his milestone goal. The Canucks pulled within 3-2 at 5:01 of the third when Kevin Bieksa scored from just in front of the net.
Nash clinched it with an empty-net goal with 18 seconds remaining.
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