A second-half strike from Will Bruin and a Ryan Gaddis own-goal in the closing stages ensured maximum points for Houston at BBVA Compass Stadium.
Dominic Kinnear's men climbed to eighth in the Eastern Conference standings with 25 points after 23 rounds as a result of their second win in three games.
The Dynamo are now just two points adrift of Philadelphia, who occupy the fifth and final play-off position in the East, though they have played a game more than Houston.
It took the home side six minutes to break the deadlock after a scoreless first half in Houston.
Bruin - Houston's leading goalscorer - was on hand to poke home the opener from close range following Giles Barnes' low cross past Union goalkeeper Andre Blake that came to the feet of the experienced striker.
It was the 25-year-old's ninth goal of the season.
Houston had a helping hand claiming all three points after Gaddis sent the ball into his own net in the 90th minute.
Substitute Omar Cummings, who replaced Bruin, sent a misguided pass which fell to Gaddis, who unfortunately put the ball past Blake.
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