In a game played in cold and windy conditions, Morrow fired a shot home from 18 yards out to notch the equalizer and give the Earthquakes (1-1-1) a standings point.
Columbus had taken the lead in the 68th when Federico Higuain's corner kick was headed home by Glauber for his first MLS goal.
The draw gave the Crew a 1-1-1 mark to begin the season.
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