On the scoring play, Clark used his head to redirect a cross into the penalty area from Jermaine Taylor past goalkeeper Zac MacMath and into the net on a play started by Giles Barnes.
Tally Hall made three saves as the Dynamo (7-6-5) used the victory to maintain their grip on the fifth spot in the Eastern Conference.
MacMath turned aside five shots for the Union (7-6-6), who remained tied with Sporting Kansas City for the third position in the East.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys