Moffat netted the equalizer with a left-footed shot at Columbus goalkeeper Andy Gruenebaum, who got a piece of it but couldn't prevent the ball from dribbling over the line.
Brad Davis also scored for Houston (12-6-7), which moved into a third-place tie with Chicago in the Eastern Conference.
Cole Grossman and Eddie Gaven scored for the Crew (8-9-5).
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