For the Union (1-2-5), it was their fourth tie in five games. The Dynamo (2-3-1) are winless in their last four.
Houston outshot Philadelphia 12-1 in the first half but couldn't score.
Dynamo defender Kofi Sarkodie received a second yellow card in the 82nd minute, which resulted in a red card and an ejection. Houston played a man down the rest of the game.
Houston was already without midfielder Brad Davis because of a sprained right ankle. It was the third straight game the six-time MLS All-Star has missed.