Vincent Nogueira sailed a free kick from just outside the box wide in the 89th minute, and Pedro Robiero hit the post in stoppage time for the Union.
Unbeaten in their last six, the Union are two points behind Columbus, which beat New England 1-0 on Saturday night, in the race for the final Eastern Conference playoff spot.
The Union and Dynamo have met three times this season, drawing both games at Philadelphia. The Dynamo won 2-0 in Houston. Houston (9-13-6) extended its undefeated streak against the Union to six games, with four wins and two draws.
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