Cooper fired home on the break to spare his side's blushes after they squandered a two-goal lead in the late stages thanks to strikes from Andrew Driver (79) and Brad Davis (83).
Two goals in as many first-half minutes from George John (34) and Andrew Jacobson (35) had seemingly put Dallas in control.
Meanwhile, in the Los Angeles derby, the Galaxy and 10-man Chivas USA exchanged late goals to play out a 1-1 draw.
Chivas played the whole of the second half a man down after Joaquin Velazquez was sent off in the 41st minute, and they appeared to be heading for defeat when substitute Jack McBean struck for the Galaxy seven minutes from the end.
But the lead lasted just six minutes before Carlos Alvarez snatched a late equaliser.