After spotting the Impact a 1-0 lead, Columbus came back with the equalizer in the 66th minute when Higuain's long-range free kick was headed into the net by Chad Marshall.
With the win, put the Crew (11-14-5) snapped a seven-game road losing streak and put themselves back into contention for an Eastern Conference playoff spot.
Marco Di Vaio scored for Montreal (13-9-6), which lost at home for the first time in seven matches.
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