The Timbers (13-5-14) got the only tally they would need when Alhassan fired a shot into the back of the net following a Will Johnson free kick.
The victory allowed Portland to snap a three-game losing streak against Seattle and tie the New York Red Bulls for the best mark in the MLS at 53 points with two games to play.
The third-place Sounders (15-11-6) dropped a third straight MLS game for just the second time in team history.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged