The former Manchester City striker got his first after just four minutes as he neatly turned a right-wing cross from Lloyd Sam into the net from six yards out.
The hosts were reduced to 10 men later in the opening period as Matt Miazga was shown a second yellow card for a cynical foul, but the visitors failed to take advantage as a David Villa volley, which flew inches wide, was the closest they came to scoring in the first half.
The Red Bulls found a second shortly after half time as Wright-Phillips converted another cross from close range.
However, he missed a fine chance to score a hat-trick later on in the half as he shot straight at the keeper when clean through on goal.
The away side gave themselves hope when substitute Patrick Mullins smashed the ball in from close range, but they couldn't find an equaliser and fell to defeat. body check tags ::