In the first meeting between the arch-rivals in the 2014 MLS season, Seattle skipper Dempsey struck in the 85th minute and then converted a penalty two minutes later as the Sounders recovered from being 4-2 down to claim a point at Providence Park in Portland.
Seattle's late comeback kept the Timbers winless in five games this season and added another chapter to the rich history between the two clubs.
Saturday's game was the 85th meeting between the Sounders and the Timbers, who also played against each other in the old North American Soccer League and first clashed in 1975.
The visitors hit the front in just the third minute with former Portland striker Kenny Cooper tapping in for Seattle after Jalil Anibaba had knocked a corner back across goal.
But in a sign of things to come, Portland continued the hectic start to the contest six minutes later with Diego Chara stealing the ball off Gonzalo Pineda before converting from the edge of the D for his first goal since September 2011.
Cooper forced Timbers goalkeeper Andrew Weber into a fine save soon after and the hosts counter-attacked immediately, with Darlington Nagbe hitting the post, before Diego Valeri gave Portland the lead in the 14th minute.
Michael Harrington picked out Valeri on the corner of the six-yard box and the Argentine midfielder spun on the ball before smashing his shot in off the crossbar from close range, but the Timbers' lead lasted just 10 minutes with Dempsey scoring his first goal thanks to an assist from Obafemi Martins.
The score remained 2-2 until half-time but 10 minutes after the break, Chara - who had suddenly got a taste for scoring again - was allowed space to push forward and slammed the ball into the top corner from 20 yards.
Portland looked to have killed the game off just two minutes later when Maximiliano Urruti picked Anibaba's pocket and then curled an exquisite shot into the top corner to give the hosts a 4-2 advantage.
The Timbers almost increased their lead again soon after when Norberto Paparatto's header slammed into the crossbar from a corner but the ball was kept out of the net by Seattle fullback DeAndre Yedlin, who was stationed on the line.
Yedlin's intervention seemed even more crucial when Dempsey struck with five minutes left plus stoppage time; the United States international poking the ball home to drag the Sounders back into the contest and Seattle's comeback was just about complete two minutes later when Ben Zemanski tripped Yedlin in the penalty area.
Dempsey made no mistake from the spot to notch his first MLS hat-trick and take Seattle to seven points from five games.
In the Texas derby, Western Conference leaders FC Dallas thrashed Houston Dynamo 4-1 with three goals in the final half hour.
Michel opened the scoring for Dallas from the spot in the first half in Houston but Dynamo were level at half-time thanks to Ricardo Clark's header.
But the visitors blew the game open after Houston's David Horst was red-carded on the hour mark with Je-Vaughn Watson heading the resultant free-kick into the net before Giles Barnes' own goal in the 68th minute put Dallas 3-1 ahead.
Watson capped off Dallas' fourth win of the season with a cool finish in the 70th minute.
An injury-hit Toronto FC showed they can win without Jermain Defoe with Michael Bradley and Issey Nakajima-Farran scoring in a 2-0 triumph at Eastern Conference leaders Columbus Crew, while Montreal Impact drew 2-2 with New York Red Bulls.
In other results, the replay of last year's MLS Cup between Sporting Kansas City and Real Salt Lake finished 0-0, Colorado Rapids defeated Vancouver Whitecaps 2-1, DC United won 2-0 over New England Revolution and Chicago Fire claimed a 2-2 draw with Philadelphia Union.
