Montreal moved past both Columbus and New England into sixth place in the Eastern Conference.
Patrice Bernier gave Montreal the lead in the 28th minute on a penalty kick, although the referee made him take three attempts before one was judged to be legal.
New England tied it in the 44th minute on a long-range blast that bounced off the bar and deflected off the legs of goaltender Donovan Ricketts into the net.
Nyassi's score came on a cross from Justin Mapp.
Montreal (7-12-3) has won two of its last three. The Revolution (6-9-4) has lost two straight.
Celebrity Families of 2014 [PHOTOS]