The former Red Bulls man appeared to use his arm, but no whistle came and he knocked home the late winner after FC Dallas lost a two-goal lead.
Dallas left its cross-state rival stunned with two set-piece goals scored in quick succession after the half hour mark. For the first, George John had the last touch when Houston defender Bobby Boswell headed Michel's free kick into the back of his head.
Mere moments later, midfielder Andrew Jacobson stabbed home David Ferreira's corner to give the home side a 2-0 lead in the 35th minute.
The goals punished Houston for failing to capitalize on a golden chance moments earlier. Giles Barnes had an opportunity to play the ball from the right to Will Bruin for a simple tap-in, but he instead elected to shoot from an angle, and Dallas goalkeeper Raul Fernandez made the easy save.
Houston managed to claw one back in the 79th minute. Kofi Sarkodie won the ball from Michel deep inside the box and crossed to newcomer Andrew Driver, who buried his shot for his first MLS goal.
The Dynamo struck again soon after to restore parity. Brad Davis pounced on the rebound after Fernandez came off his line to meet Driver's low cross but failed to collect the ball.
Dallas came back with a vengeance and a fairytale ending. Cooper got away with what appeared to be a handball when he received a high ball inside the penalty area, but he kept on playing and touched his shot past Dynamo goalkeeper Tally Hall for the 90t- minute winner.
The win was just Dallas' fourth in 20 regular-season meetings with the Dynamo. Houston, meanwhile, awaits word on a potential injury to Bruin, who limped off in the 49th minute.