After starting the season winless in their first six matches, the Red Bulls have come on as of late to win two straight following a 2-1 victory over the Philadelphia Union last week.
Houston had the better of the energy in the first 10 minutes, but it quickly evaporated in the 12th minute when Thierry Henry sent a quick, low cross into the area for an easy volley into the net by Wright-Phillips to get the hosts off and running.
12 minutes later the Red Bulls doubled their advantage. Roy Miller did well to fight through a tackle on the left flank by Warren Creavalle before sending a cross into the area for another easy finish by Wright-Phillips.
Houston's best chance of the first half came in stoppage time when the ball fell to the feet of Andrew Driver in the box, but the shot sailed well over the crossbar.
The visitors came out with energy in the second half and were creating some chances early, but were wasteful, while New York displayed clinical finishing all night and made it 3-0 in the 65th minute.
Wright-Phillips was again involved in the goal as his cross from the right wing was parried by a diving Tally Hall, but the ball went straight to the feet of Henry, who calmly blasted it into an empty net.
Wright-Phillips completed his treble with four minutes to play when he converted a penalty kick after Henry was taken down in the box by Houston's Tony Cascio.
The result lifts New York into third place in the Eastern Conference with 10 points, while Houston's winless run has reached five games and the club hasn't scored a goal in 319 minutes.