Houston almost regained the lead when Davis released the run of Oscar Garcia in the inside right channel in the box and his shot almost squirmed under Luis Robles, but the keeper managed to gather the ball before it crossed the line.
After the break, the Red Bulls upped the ante and exerted pressure on the home side. Tim Cahill nearly handed his side the lead when he latched on to Thierry Henry's cross, but his volley smashed off the post and went wide.
The visitors did go ahead though in the 72nd minute as Wright-Phillips notched his second of game, guiding his header beyond the reach of Hall after latching on to Ambroise Oyongo's cross from the left.
However, Houston were handed a lifeline late in the game when Chris Duvall was adjudged to have handled the ball in the area and a penalty was awarded. Davis took the spot kick and placed the ball past Robles to earn his side a point.