New York (6-3-1) won its third in a row and jumped past D.C. United into second place in the Eastern Conference -- two points behind Kansas City.
Cooper received a pass at the top of the box in the 7th minute, but was overwhelmed by three defenders and lost possession.
Houston's Corey Ashe, however, sent a lazy pass back to goaltender Tally Hall. Cooper beat Hall to the ball and drove it past the goalie into the net.
The Dynamo's winless streak reached five games (0-3-2). Houston has won just twice in nine games this season and is in seventh place in the East.