After missing out on a 0-0 draw in the first leg through suspension, Dempsey came up big for the home side in the second leg Thursday.
The 34-year-old came close with a volley in the first half, getting on the end of a Nicolas Lodiero cross and pulling it just wide of the mark.
But the Texan found the mark midway through the second half, finishing off a Seattle move with a left-footed shot into the corner to put his side in front.
The former U.S. captain then finished the tie off with his second of the night, touching home a cross from Victor Rodriguez to double the lead.
Dempsey and the Sounders will now make use of the international break to get healthy — with Osvaldo Alonso and Jordan Morris among their injury concerns — before taking on the Portland Timbers or Houston Dynamo in the Western Conference final.