Despite being on the road for the midweek contest, the visiting side stormed out to a 2-0 lead inside the opening 15 minutes.
Bradley Wright-Phillips opened the scoring in the seventh minute, taking the ball down and rounding Chicago goalkeeper Matt Lampson before slotting home. The goal was the 99th for Wright-Phillips in all competitions for the Red Bulls.
Sacha Kljestan doubled the lead in the 11th minute, sliding in to finish a Tyler Adams cross from the right side to give his club a commanding lead early in the one-off playoff contest.
Daniel Royer tacked on New York's third of the night with a calm turn and finish in the 70th minute.
And a fourth from Gonzalo Veron in the final minutes of the match gave the game its final 4-0 scoreline.
The Red Bulls will face Supporters' Shield winner Toronto FC in the Eastern Conference semifinals.