After failing to score in the home leg of their CCL semifinal against Chivas on Tuesday, Jesse Marsch's side got goals from Bradley Wright-Phillips, Alejandro "Kaku" Romero Gamarra and Michael Murillo.
A poor Victor Cabrera allowed Florian Valot to play Wright-Phillips in on goal for the opener in just the fifth minute.
But the visitors were able to respond after the half-hour mark when Jeisson Vargas delivered a fine free kick off the post and in for the equalizer.
The Red Bulls saw a shot cleared off the line and another hit the crossbar but finally found their second in the 57th minute when Wright-Phillips set up Kaku to score with a first-time shot.
It was the first MLS goal for Kaku, the 23-year-old Argentine who signed as a designated player in February.
New York wrapped up the win in the 76th minute when Kemar Lawrence sent a low cross through the six-yard box and Murillo was on hand to tap home.
New York 3-1 Montreal: Red Bulls bounce back - Via MLS
After being knocked out in the CONCACAF Champions League semifinals, New York Red Bulls overcame Montreal Impact with a dominant second half.