The victory brought the visitor within two points of the first-placed Sounders in the MLS Western Conference table, with one fewer match played.
KC captain Johnny Russell set the tone in the 31st minute with a beautiful free kick from just outside the area to give the visitors the lead, and Daniel Salloi doubled the advantage before half-time.
After Fredy Montero answered for Sounders in the 51st minute, Cameron Duke sneaked behind the defence in the 72nd minute to seal the win.
KC is unbeaten in its last five matches and has only one loss in its last 10.
A brace from Gustavo Bou helped New England Revolution expand their lead atop the Eastern Conference with a 2-1 win over Montreal.
Kacper Przybylko found the net for the third straight game, putting home a rebound in the 85th minute to salvage a 1-1 draw for Philadelphia against Inter Miami as Phil Neville's side remain bottom of the table.
New York City FC matched its season-high in goals, scoring four times after the break in a 5-0 demolition of Orlando City.
Ola Kamara's 27th-minute goal gave DC United a 1-0 victory over New York Red Bulls.