Bradley Wright-Phillips took the penalty kicks for the Red Bulls (4-5-5) in the fifth and the 65th minutes — and both went waist high and to Ousted's right.
Kekuta Manneh opened the scoring with a close-range goal in the 15th minute, and Kianz Froese added another for the Whitecaps (9-6-2) with a breakaway in the 77th.
Anatole Abang pulled New York back within one in the 82nd, but Ousted made his most difficult save of the match a minute later, diving and deflecting Manolo Sanchez's low-skipping shot out of play.
Vancouver moved into a first-place tie with Seattle in the Western Conference.
Sacha Kljestan picked up the red card in the 11th when he elbowed and tripped Kendall Waston.
The Red Bulls lost their fourth league match in a row.