The victory sends the Red Bulls into the conference final, where they will face the winner of Sunday's game between Orlando City and Atlanta United.
Uruguayan Felipe Carballo fired the New Jersey-based side ahead in the 16th minute of the "Hudson River Derby" when a headed clearance fell to him over 20 yards out and he brought the ball down masterfully before blasting into the top corner.
Nine minutes later, the Red Bulls doubled their advantage when, from an Emil Forsberg corner, the ball fell to Belgian Dante Vanzeir, who drilled a crisp, low shot in off the inside of the post.
The game was played at Citi Field, home of the New York Mets baseball club given that NYCFC's usual home at Yankee Stadium was unavailable.
The home side struggled to get a grip on a frantic game but Alonso Martinez had two opportunities before the interval.
After good work from Kevin O'Toole, the Costa Rican saw his shot from close range smothered by Red Bulls keeper Carlo Caronel.
Then James Sands played in a dangerous low ball from the right but Martinez's attempt flick was too weak to truly trouble Caronel.
NYCFC came out strongly after the break with Martinez forcing another save out of Coronel in the 48th minute and then a minute later Keaton Parks headed over.
Austrian Hannes Wolf worked himself into a promising position down the right but his diagonal effort flew wide of the far post.
NYCFC piled on the pressure in the latter stages, but with Paraguay international Coronel in strong form and the Red Bulls defence tenacious, they were unable to find a way through.
Founding members of MLS in 1996, the Red Bulls have never won MLS Cup and qualified for the playoffs this year after finishing seventh in the East.
Later on Saturday, in the Western Conference semi-finals, Los Angeles FC take on the Seattle Sounders.
