Nguyen, who earlier had failed on a penalty shot opportunity when he was fouled by Dejan Jakovic, made good on his second opportunity following an infraction by Lewis Neal.
United had grabbed the lead in the 11th minute when a low cross from Luis Silva was tipped into the New England goal by Revolution defender Scott Caldwell.
It took the Revolution just a minute to wipe out D.C.'s advantage. Diego Fagundez narrowly beat an offside trap to snare Saer Sene's through ball and directed a shot past Hamid for his 11th goal of the season.
New England now leads Chicago by one point with 40 points. D.C. United lost for the 20th time this season and sits at the bottom of the league standings with 15 points.