Nyassi notched the goal after a reeling off a long run and launching a shot that found the upper corner of the net.
Goalkeeper Troy Perkins -- making his Impact debut after being acquired from Portland -- preserved the shutout with a key save on New England's Saer Sene in the 70th minute.
The victory gave expansion Montreal (10-13-3) hope as it pushes to make the Eastern Conference playoffs.
The Revolution (6-12-5), meanwhile, absorbed its fifth loss in six games.
2014: The Year in Music [PHOTOS]