Discipline problems plagued the Texas side as it saw a lead fall away late in Portland.
Dallas scored in the 27th minute to take the lead. Fabian Castillo chested down a ball into the box and turned outside a pair of Portland defenders to hit his shot past Donovan Ricketts.
Blas Perez doubled the visitors' lead shortly before halftime. Tesho Akindele scorched the Timbers down the right wing and his cut-back pass was dummied by Castillo for Perez, who shot almost completely unmarked from the top of the box past Ricketts.
The Timbers were awarded a penalty in the 78th minute when Je-Vaughn Watson was called for clipping Fenando Adi in the wide area of the penalty box. Will Johnson converted from the spot to give the Timbers hope.
Dallas, already under pressure, had to play a man down after Moises Hernandez was sent off for a stamp on Danny O'Rourke in the 89th minute. Blas Perez picked up a red of his own in stoppage time after an altercation with Pah Modou Kah.
Kah got his own back with the equalizer, bundling the ball into the net from three yards out.
Dallas's disciplinary issues didn't stop at the final whistle, as Castillo had to be restrained in a confrontation with an assitant referee.