With the first leg locked at 0-0 at the hour mark Sunday, Matteo Mancosu banged home a top-class goal after collecting a direct ball between two defenders.
The Impact held on amid a frantic finish, as Bradley Wright-Phillips missed a golden opportunity in stoppage time and Red Bulls substitute Omer Damari earned himself a straight red card for a rash tackle on Calum Mallace.
Montreal visits Red Bull Arena for the second leg next Sunday.
