Wright-Phillips had three goals, while Henry was masterful in a more creative role as New York steamrolled a poor Houston team.
Thierry Henry combined well with the Englishman, and involved himself on all four goals to lead the home team past the Texas club.
Wright-Phillips scored the opener for New York in the 12th minute, connecting with Henry's low cross in front of goal and applying the simple finish.
He picked up a second in the 24th minute. Roy Miller beat Warren Creavalle to Henry's long diagonal pass and whipped in another low cross to Wright-Phillips for the forward's second of the game.
Henry himself did the honors to slot home the third, playing a wide ball then slipping past an unresponsive Creavalle to finish Wright-Phillips' cross in the 65th minute.
Wright-Phillips converted a penalty to complete his hat trick in the 86th minute atfer Thierry Henry was pulled down in the box by Tony Cascio.
New York moves up to third in Major League Soccer's Eastern Conference with a 2-2-4 record. The 2013 MLS Supporters' Shield winners have won their last two matches. 2-4-1 Houston is winless in its last five games after starting 2014 with a pair of wins.