The hosts continued to dominate after taking the lead, but they missed the chance to double their advantage when Aurélien Collin headed wide of the target while in space inside the box.
New York struggled to create opportunities in the first half, and were forced to wait until after the interval to cause their rivals any problems.
Their first clear chance of the match fell to Wright-Phillips, who took full advantage of space on the edge of the box to drill home the equaliser.
Wright-Phillips could have doubled his personal tally moments later, but his low effort was easily saved by Eric Kronberg.
Dominic Dwyer was agonisingly close to restoring Sporting's lead when he lost his marker inside the box before heading over the crossbar.
Red Bulls forward Thierry Henry saw a late strike well saved by Kronberg as both sides searched for the winning goal, but they were unable to be separated in the closing stages.