Nielsen finished with five saves, including a near-post stop of New York's Thierry Henry in the 65th minute.
With the draw, Kansas City improved to 17-7-9 and secured the East title.
New York goalkeeper Luis Robles needed to make only one save. It came in the 86th when he stopped Kei Kamara's header off a cross from Graham Zusi.
The Red Bulls (15-9-9) also nailed down a playoff berth with the draw, coupled with the Columbus Crew's loss to D.C. United Saturday.