Herculez Gomez opened the scoring for the MLS side as he netted from the penalty spot just before half time, while Jordan Morris added two more goals to the scoreline after coming on as a second-half substitute.
The breakthrough was made three minutes before the break when Hammers goalkeeper Adrian was punished for bringing down Gomez, who was through on goal after latching on to Aaron Kovar's pass.
The 34-year-old forward converted from the spot by sending Adrian the wrong way, and the Sounders continued their dominance in the second half.
Morris nudged the ball into the back of the net off the rebound after Oalex Anderson's shot was blocked, and he scored another just two minutes later.
Joevin Jones's ball found the forward, who smashed it home from six yards out, in the 72nd minute.
West Ham, who were without Dimitri Payet due to the midfielder playing at Euro 2016 with France, made 10 changes during the friendly, while Seattle made nine.