Maxi Moralez opened the scoring after just six minutes and Heber doubled the lead late in the first half. Talles Magno added a third from the penalty spot before Djordje Mihailovic found the back of the net in the 86th minute for the hosts.
The win sends NYCFC to the Eastern Conference finals for the second straight year where they will face top seed Philadelphia in a rematch of last year's 2-1 victory by the Boys In Blue.
Story of the match
NYCFC interim boss Nick Cushing named an unchanged side from the one that defeated Miami in the first round last Monday.
Within six minutes, the defending champions were on top. A neat one-two by Gabriel Pereira and Santiago Rodriguez culminated with the Brazilian beating Montreal goalkeeper James Pantemis to the through ball and clipping back across the face of goal.
Moralez then fired home from close range for his second goal in as many playoff matches this season.
Johnson was in top form and he clawed away Ismael Kone's effort before Samuel Piette and Kemal Miller unsuccessfully tried their luck from distance.
Montreal was having the better of the play, but were caught out on the counterattack as Rodriguez won the ball back on the edge of the box, passing to Moralez, who returned it to the Colombian and he sent an inch-perfect pass to Heber, who slid the ball past Pantemis.
Early in the second half, Montreal manager Wilfried Nancy introduced leading scorer Romell Quioto, but it was the Boys In Blue holding firm in defense and threatening when on the counter.
Heber nearly grabbed his second and NYCFC's third, firing straight at Pantemis, but it wasn't long after that than the visitors found a third just after the hour mark.
Substitute Talles Magno sent the ball into the path of Pereira, who was fouled by Pantemis and after the referee pointed to the spot, Magno stepped up and calmly put the ball, and the match, away.
With four minutes remaining, Montreal did pick up a consolation goal, Zachary Brault-Guillard's delivery finding Mihailovic, who nodded past Johnson.
Despite some late pressure, the Boys In Blue stood firm and continued their roll through the Eastern Conference playoffs.
Man of the match: Sean Johnson
For someone as good as he is, Johnson often gets overlooked because of the firepower NYCFC has, but the rare times Montreal threatened, the American international came up big with key saves.