Cahill's tally in the 38th minute broke a 1-1 tie and put the Red Bulls (12-9-6) ahead to stay.
Robles preserved the lead in the 73rd minute when he stopped a penalty kick try by Dwayne De Rosario after a foul and a red card was handed out to Ibrahim Sekagya.
Lloyd Sam also scored for New York, which ended three-game winless skid.
Nick DeLeon scored for United (3-18-5).
2014: The Year in Music [PHOTOS]