Wright-Phillips won the MLS Golden Boot last term with 27 regular-season goals, which saw the Englishman become the club's new Designated Player following Thierry Henry's departure.
And after firing a blank in the Red Bulls' 1-1 draw at Sporting Kansas City a fortnight, the 30-year-old found the net against United at Red Bull Arena.
Wright-Phillips opened the scoring in the 25th minute after demonstrating some impressive close control inside the penalty area.
Dax McCarty played a long ball over the top of the United defence, picking out Wright-Phillips, who flicked it over Steve Birnbaum before firing low and hard past goalkeeper Bill Hamid.
The Red Bulls put the result beyond doubt with 20 minutes remaining, Lloyd Sam - on target against Sporting KC - beating Hamid at his near post.
Jesse Marsch's men are second in the East, one point adrift of city rivals New York City, while United are a point further back in sixth position.
Sunday's only other fixture saw East cellar-dwellers Chicago Fire crash to their third loss of the season, defeated 2-1 by the San Jose Earthquakes.
Fire conceded two goals inside the opening 21 minutes and they never recovered, despite a spirited performance in the second half.
San Jose hit the ground running at Avaya Stadium, where Fatai Alashe headed the ball into the net from point-blank range in the fifth minute.
Ty Harden doubled the home side's lead 16 minutes later via a rebound after Fire keeper Sean Johnson fumbled Clarence Goodson's volley.
Harrison Shipp reduced the deficit in the 29th minute but it proved to be in vain as the Earthquakes moved second in the Western Conference behind FC Dallas with six points from three matches.
