The Earthquakes' tally came on an own goal by Houston's Zarek Valentin.
The Earthquakes have recorded four straight ties as part of an 11-match winless streak (0-6-5).
The Dynamo remained winless on the road this season at 0-4-5. The draw also stretches Houston's winless streak to eight matches (0-2-6).
Tensions were high after the match and both sides needed to be restrained.
Fierro was ejected with a red card in the seventh minute of the eight-minute stoppage time due to violent conduct.
San Jose held a 12-10 edge in shots, but Houston had five shots on goal to San Jose's two.
Houston took a 1-0 lead in the 40th minute on the goal by Vera. The goal was Vera's second of the season.
Vera was well outside the box when the ball came in his way and he unleashed a rocket that sailed into the right corner past Marcinkowski.
The Earthquakes knotted the score in the fifth minute of first-half stoppage time. Cristian Espinoza sent the ball toward Oswaldo Alanis in front of the net but Valentin got his right foot on the ball and it bounced into the net to tie the score.
San Jose's first shot on goal came in the 65th minute when Luciano Abecasis delivered a left-footer that was saved by Maric.
Alanis put a left-footed free kick on goal in the 82nd minute but Maric easily made the save.
Two minutes later, Rios sent a short right-footed shot just over the crossbar.