Casey put the Union ahead to stay in the 7th minute on header off a cross from Sheanon Williams at the edge of the box.
He doubled the advantage in the 64th minute with his fourth goal of the year as the Red Bulls were down a man following a red card issued to Lloyd Sam. On the play, Casey collected the rebound of a Keon Daniel shot and sent it past goalkeeper Luis Robles.
Antoine Hoppenot also scored for Philadelphia (7-5-4), which broke a five-game losing to New York and moved into a second-place tie with the Red Bulls at 25 points.
New York (7-6-4) fell to 6-3-0 all-time against the Union.