The game had started promisingly when Thierry Henry headed just over the bar in the second minute.
Fabian Espindola's 14th-minute goal looked like it would be enough for a Red Bulls win, but Lee Nguyen's 85th-minute penalty after Jamison Olave's hand ball kickstarted a frantic final few minutes.
New England had Andy Dorman sent off seconds later but somehow took the lead in the first minute of stoppage time through Diego Fagundez right-footed drive, which was too good for New York keeper Luis Robles.
The Red Bulls did have a great chance to equalise when, with Revs keeper Matt Reis on the ground, substitute Andre Akpan skied his shot with the goal begging.
However, in the 97th minute of the game former Everton midfielder Tim Cahill rose to head home a vital equaliser, which puts his team into the playoffs.
For the Revolution, they may feel the late equaliser is a big blow to their own hopes of reaching the MLS Cup stages having started the game a point outside the playoff positions.