Boyd scored in the 16th minute thanks to a run behind the Seattle defense and an accurate cross from Steven Smith, putting the ball into an empty net.
Horst doubled the lead 9 minutes later when he headed a Franck Songo'o corner kick into the net.
The Timbers (4-6-4) came up with just enough defense in the second half to notch their first MLS victory over bitter rival Seattle.
The Sounders (7-5-4) got a 58th-minute goal from Eddie Johnson but it wasn't enough to prevent their club-record winless streak in league play from reaching seven games.
The game erupted into fights during stoppage time, when Seattle's Fredy Montero was given a red card for leveling Horst. Also ejected was Portland defender Lovel Palmer, who elbowed Johnson during the scuffle.