It took New York just 12 minutes to break the deadlock thanks to Wright-Phillips, who lost his marker inside the box to tap in an inch-perfect cross from Thierry Henry.
Wright-Phillips benefited from another defence-splitting pass in the 24th minute when he was able to drill the ball home from Rory Miller's delivery.
The former Manchester City forward should have completed his hat-trick before the interval, but he failed to beat Tally Hall after linking well with Henry once again.
Houston applied pressure after the break, but their progress was once again halted by Robles, who pushed a low effort from Bruin past the post.
Despite dominating the early stages of the second half, Houston's hopes of fighting back were dealt a further blow in the 65th minute when Henry collected a loose ball before firing his side's third goal past a helpless Hall.
The Red Bulls were gifted the opportunity to add a fourth with just four minutes of normal time remaining when Henry was brought down inside the box by Tony Cascio.
Wright-Phillips stepped up to convert from 12 yards and complete his hat-trick on a comfortable evening for New York.