Western Conference winners Dallas trailed 2-1 to Sounders after the first leg in Seattle a week ago, and it was the visitors who started on the front foot as Andreas Ivanschitz forced a save from Jesse Gonzalez.
The Texan side had won nine of their last 10 home matches, however, and they had their first sight of goal midway through the first half when top scorer Fabian Castillo nutmegged a defender and fired a rasping effort over the crossbar from distance.
Sounders were unfortunate not to take the lead when Tyrone Mears's whipped ball across goal narrowly evaded everyone in the penalty area, before Michael Barrios saw his half-volley held by Stefan Frei and Gonzalez had to tip Nelson Valdez's deflected shot over the bar on the stroke of half time as both teams had further chances.
The frantic pace continued after the break and Frei produced a fine reflex save to deny Castillo from close range as Dallas dominated possession in the second half, and they went ahead on away goals when substitute Tesho Akindele headed home his first touch of the ball to put his side in front on the night.
That lead lasted just six minutes, however, as Chad Marshall headed in from a corner to seemingly put Seattle into the final, but a remarkable final few minutes of the 90 contained another twist when a corner at the other end led to Walker Zimmerman turning home from close range to send the game to extra time.
Both teams looked understandably fatigued as the extra 30 minutes got under way after the dramatic finale to regulation time, with Akindele's curling effort the only chance of note in the first half.
Frei denied Akindele with a smart stop four minutes from time as the tie headed to penalties, and when Gonzalez saved from Ivanschitz and Marshall, Zimmerman converted to send Dallas into their first Conference final since 2010 and break Seattle hearts.