Fernandez made his best save in the 45th minute when he turned aside Daniele Paponi's low shot off a pass from Davy Arnaud.
FCD (8-5-8) earned the point despite being outshot by Montreal 15-6, but remained without a win for eighth straight game and was scoreless for the fourth consecutive contest.
Troy Perkins made two stops for the Impact (9-5-5), whose own winless streak extended to five matches.
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