The Sounders, who took a 1-0 lead in the 27th minute when Joevin Jones scored on his own rebound, played a significant chunk of the game a man down after Brad Evans was red-carded late in the first half.
The scorching heat caused by a heatwave in the Pacific Northwest meant that kickoff had to be delayed, but Seattle showed great character and even better fitness levels to stay in the game and they were rewarded when Dempsey rose above Amobi Okugo in the 94th minute to head in a Roman Torres cross to ensure the points were shared.
Portland had the game's first notable chance in the 11 minute off one of their patented counterattacks that ended with midfielder Diego Chara setting up forward Adi with a chance on Sounders goalkeeper Stefan Frei.
Fanendo Adi scored from the spot, and Dairon Asprilla had time to add a second before the halftime whistle for the Timbers. The rivalry dates to 1975 when the teams were with the old North American Soccer League, but fans of the three teams christened the Cascadia Cup in 2004.
The Timbers tied it at 1 in the 44th minute on Adi's penalty kick. Vancouver are the defending Cascadia Cup champions.
UK prime minister wins N Ireland party's support govt
The money is going to address issues near and dear to the 1.8 million people of Northern Ireland. May and DUP leader Arlene Foster presided at the signing of a deal at Downing Street on Monday.
The Timbers almost added a third goal after some confusion at the back from the Sounders, but Chad Marshall was able to usher the ball out for a corner shortly before taking a ball to the face, causing a brief halt in play. He upped his total this season to nine goals.
Dempsey, Seattle's leading scorer against the Timbers with nine goals, came in as a sub in the 56th minute.
The Sounders won the first league match between the teams 1-0 on May 27, then won a fourth-round U.S. Open Cup match 2-1 earlier this month.
Seattle leads the series in MLS 9-5-5, and the all-time series 50-35-13.
It was Portland's 116th consecutive sellout.
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