On the play, Cahill popped a header into the net after Crew goalkeeper Andy Gruenebaum had made a big stop on a shot by Jonny Steele.
The tally came 8 minutes after Red Bulls goalie Luis Robles made a diving save on a penalty kick try by Federico Higuain.
New York (5-4-2) notched a third straight victory.
The Crew (3-3-3), meanwhile, lost at home for the first time in 13 contests.
Workers accuse National Zoo of animal mismanagement
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees