Higuain put the Crew on top in the 62nd minute on a penalty kick after Jamison Olave was handed a controversial penalty for a push in the 18-yard box.
He doubled the advantage in the 76th minute after getting a feed from Wil Trapp and chipping the ball over onrushing Red Bulls goalie Luis Robles.
Columbus (7-11-5) posted its first victory since July 7.
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