With Salt Lake down a man due to a red card handed out to Abdoulie Mansally, Dallas erased a 1-0 deficit when second-half substitute Je-Vaughn Watson moved down the left wing and Cooper got hold of the ball for a goal.
Despite the tie, Dallas (10-10-11) all but fell out of post-season contention.
Alvaro Saborio scored in the 60th for RSL, which moved to 15-10-6 in its bid for the best record in the MLS.
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