Marco Di Vaio forced a Houston turnover and played a through-ball to Nyassi who scored on his own rebound for the expansion Impact (12-15-5), who were nevertheless eliminated from the post-season.
The Dynamo appeared to have won the contest in stoppage time when Brian Ching scored, but after an officials' conference he was ruled offside.
Will Bruin scored in the 44th for Houston (13-8-11), which missed a chance to strengthen its bid for the Eastern Conference's fifth and final playoff spot.
The Dynamo's fate will be determined Sunday when the Columbus Crew plays Sporting Kansas City. Should the Crew win, they will surpass Houston by a point and vault into the fifth spot.
Rosie O'Donnell unveils nearly 50-pound weight loss
Members of Congress to keep receiving porn magazine