Carter's three-goal performance, the fourth of his career, boosted Columbus to its first win in three contests.
The Sharks got two markers from Logan Couture and Joe Thornton added a goal in their fourth straight setback.
Antti Niemi was yanked from net after yielding three tallies on just 11 shots.
Thomas Greiss let in three goals on 24 shots the rest of the way for the Sharks.
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