Casey first struck in the 35th minute, controlling a pass from Sebastien Le Toux, getting past a pair of defenders and slotting the ball behind D.C. goalkeeper Bill Hamid.
He doubled the advantage in the 75th minute, converting a cross from Fabinho.
Philadelphia (10-7-7) moved into third place in the Eastern Conference.
Last-place United fell to 3-16-4.
Notable deaths of 2014 [PHOTOS]