Trailing 2-0 in the second half, the Dynamo (1-1-0) got goals from Andrew Driver in the 79th minute and Brad Davis in the 83rd to forge a late deadlock.
But Dallas (2-1-0) went back in front in the final minute.
On the decisive play, Michel sent a cross over the head of Je-Vaughn Watson that Cooper tried to strike with a header but missed. The ball landed at his feet and he fired it home for his first goal of the season.
Houston protested that Cooper played the ball with his arm on the play.
George John and Andrew Jacobson also found the net for FCD.