The Galaxy were 2-1 losers in the second leg of the Eastern Conference Final at CenturyLink Field on Sunday but Juninho's solitary 54th-minute goal was enough to see the four-time champions through to the decider.
Bruce Arena's Galaxy - winners of the MLS Cup in 2002, 2005, 2011 and 2012, will host New England Revolution in the MLS Cup at StubHub Center on December 7.
The Galaxy held a slender one-goal lead heading into the return leg in Seattle but that advantage was quickly erased as Supporters' Shield champions the Sounders took control in front of a record play-off crowd of 46,758.
Seattle midfielder Brad Evans put the Sounders ahead on the night and level on aggregate after 26 minutes.
Some neat interchange play saw the ball fall to captain Clint Dempsey, who squared it across goal for Evans to poke home from inside the six-yard box.
It got better for the home side four minutes later as Dempsey took his tally to 16 goals for the season.
The United States international pounced on a rebound from the edge of the penalty area, firing the ball underneath Galaxy goalkeeper Jaime Penedo, who failed to keep it out.
While the Sounders led 2-0 at half-time, the Galaxy were always just one goal away from regaining the advantage and it took just nine second-half minutes for the Los Angeles outfit to silence the home crowd.
Brazilian midfielder Juninho sent a low half-volley into the bottom corner of the net in the 54th minute - a goal that ultimately booked the Galaxy's spot in the decider.