Jordan Morris' scrappy header in the 113th minute gave Seattle a remarkable 4-3 win on Saturday at CenturyLink Field and prevented what seemed to be an inevitable shootout.
Morris clinched his hat-trick and the Sounders ensured their place in the Western Conference semifinals. They'll face Real Salt Lake on Wednesday.
Goalkeeper Stefan Frei played his part, producing five saves in extra time to keep Dallas at bay. Frei didn't make a single stop until the 96th minute.
Seattle took the game to the visitors early.
Morris made it 2-0 for Seattle after a long ball caught Dallas off guard.
But Dallas had an answer to Seattle's early assault. USMNT international Reggie Cannon scored his first MLS goal to halve the Sounders' lead six minutes from the interval, the full-back converting from close range amid calls for a handball.
The next three goals all came from corner kicks. Matt Hedges outleaped Gustav Svensson to direct Michael Barrios' delivery beyond Frei and tie the game in the 64th minute. Hovering in the six-yard box, Morris responded 10 minutes later with the flick of his left foot.
Bryan Acosta took advantage of Frei's questionable positioning to nod in the latest equalizer and send the game to extra time.
But Morris made sure the lead only changed one more time.