The former Manchester City, Southampton and Charlton Athletic forward received a ball from fellow Englishman Lloyd Sam on the left side of the area in the 66th minute before firing in off the post to cancel out Jairo Arrieta's 39th-minute penalty.
The equalizing goal comes just three days after Wright-Phillips netted a hat-trick in New York's 4-0 win over Houston Dynamo and he was delighted to have some luck in goal after a difficult beginning to the campaign.
"I ended up getting a good touch on it and getting a good strike on goal because I let two in the first half get away so I wanted to get one on target," Wright-Phillips said.
"Two weeks ago that probably would have got blocked and gone the other way on the attack. That's how football goes, especially for strikers. We score a few games, then you don't."
Wright-Phillips has now hit the back of the net five times in eight appearances for the Red Bulls this season to take his MLS tally to seven goals from 17 outings.
The Red Bulls have played nine times this term for two wins, five draws and two losses which has them sitting fourth on the Eastern Conference table.
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