With the win, the Red Bulls moved two points behind Eastern Conference-leading D.C. United.
Lloyd Sam opened the scoring in the 33rd minute.
Wright-Phillips made it 2-0 when he blasted a volley, off a cross from Mike Grella, into the top-right corner from just outside the box. Wright-Phillips capped the scoring in the in the 64th when he slipped behind the defense and, after a slight hesitation to avoid being offside, found the back of the net on a right-footer from the center of the box.
In Sunday's other game, Obafemi Martins scored his 10th goal of the season in the opening minutes and Brad Evans converted a disputed penalty just before halftime as the Seattle Sounders beat the Portland Timbers 2-1
Seattle earned a much needed three points in the Western Conference playoff race before a crowd of 64,358, the fourth largest crowd for an MLS game in Sounders' history. Seattle started the day in seventh place and outside of the playoff picture, but pulled into a tie with San Jose for sixth with the victory.
Martins beat goalkeeper Adam Kwarasey in the sixth minute to give Seattle the early lead, then earned the Sounders a penalty kick in the 42nd minute when he was taken down in the box by Kwarasey. Brad Evans converted the penalty kick for his first goal of the season.
Jack Jewsbury scored off a corner early in the second half for Portland.