Greiss, who last started Dec. 3, raised his record to 5-4 with a 24-save performance. The Sharks won their third in a row.
The game-winning goal came 4:44 into the second period from Joe Thornton.
Columbus remained stuck on 10 wins for the season, tied with Anaheim for the fewest in the NHL. Curtis Sanford allowed two goals on 39 shots.
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