Cooper's goal came in the second half of extra time after Darlington Nagbe's goal in the final seconds of regulation forced an additional 30 minutes of play. Gonzalo Pineda sent a pass into the penalty area from 30 yards out and Cooper was able to flick it past Portland goalkeeper Donovan Ricketts.
Seattle held on over the final minutes, helped by the Timbers playing a man down after Diego Chara was given a red card in the 99th minute for his tackle of Seattle's Marco Pappa.
Pappa added an insurance goal in the 116th minute.
Osvaldo Alonso scored in the 69th minute to give Seattle a lead that held up until Nagbe's goal in second-half stoppage time.
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