In the third minute of second-half stoppage time, a flicked header from Red Bulls substitute Tim Cahill found Wright-Phillips in the penalty area and the English forward made no mistake with his volley to ensure a 2-2 draw for Mike Petke's team at Red Bull Arena.
Toronto had come from behind to lead 2-1 thanks to goals from Jermain Defoe and Gilberto but were denied a third straight win in the MLS due to Wright-Phillips' late intervention.
The draw also guaranteed that New York stayed within a point of Toronto in the Eastern Conference, while the Red Bulls also claimed the fifth and last play-off spot in the East, pushing the Columbus Crew down to sixth.
The Red Bulls led 1-0 at half-time thanks to Peguy Luyindula's strong header in the 36th minute but the visitors levelled 10 minutes after the break when Defoe struck Dominic Oduro's cross into the net.
Defoe's eighth goal of the season gave Toronto some momentum and they hit the front with 18 minutes left.
A free-kick just outside the box sparked a heated argument between Defoe and Gilberto over who would take the shot.
Gilberto did not back down, having claimed the ball first, and the Brazilian 25-year-old unleashed a bullet of a shot that found the roof of the net and left Defoe laughing with embarrassment.
But Toronto were unable to hold onto their 2-1 lead, with Cahill's flick in his first game back from the FIFA World Cup helping steal a point for the home side.
Also on Friday, reigning champions Sporting Kansas City regained top spot in the East with a 1-0 win at Portland Timbers.
Lawrence Olum's first-half strike after a goal-mouth scramble gave Sporting the win at Providence Park, as Kansas City moved up to 25 points, ahead of DC United on goal difference.
New England Revolution (23 points) sit third, three points ahead of Toronto, who have a one-point gap on the Red Bulls.
