The Revolution had grabbed a seemingly decisive 2-1 lead 2 minutes into the second-half stoppage time when Diego Fagundez scored after a giveaway by New York defender David Carney.
But Cahill struck on the game's final play, converting a looping header into a score-tying tally for the Red Bulls (15-9-8), who came into the game with a four-point advantage atop the East and clinched a post-season berth.
Fabian Espindola scored New York's other goal.
Lee Nguyen added a goal for the Revs (11-11-9), who remained winless in New York for a sixth straight season.
Notable deaths of 2014 [PHOTOS]