Less than two minutes after coming into the game, Cooper converted a pass from Obafemi Martins. Martins also set up Lamar Neagle for the tying goal in the 62nd minute. He now has an MLS-leading six assists.
Cooper subbed in for Neagle in the 86th minute. With Martins taking the ball down the left wing, Cooper ran into the box, took Martins' cross and one-timed it high into the left side of the net for his third goal of the season.
The Sounders (7-2-1) tied a club record with their fifth consecutive victory, extending their unbeaten streak to six and their league-leading point total to 22. They came from behind in five of the games during the unbeaten streak.
Brazilian forward Michel gave FC Dallas (5-4-1) the early lead when he converted a penalty kick in the 16th minute. It was his fourth goal of the year.
Blas Perez helped set up the penalty kick when he charged into the box in pursuit of the ball, with Brad Evans and Zach Scott of the Sounders on him. In a tangle of feet, Perez went down, with Evans whistled for the foul. Michel stepped up and drilled the spot kick past Seattle goalkeeper Stefan Frei.
Clint Dempsey started the play that led to Neagle's tying goal, passing the ball from the middle of the field to Martins on the right side. Martins crossed it into the penalty area, and Neagle converted from just outside the 6-yard box for his fourth goal of the year.