Portland captured the two-game series by an aggregate score of 5-3, moving the Timbers into the conference finals against Real Salt Lake.
The first leg of the finals will be held on Sunday in Utah.
With Portland having downed Seattle in the first game of the semifinal series 2-1, the Sounders needed to take charge early in the second contest.
Instead, it was Will Johnson who scored for Portland in the 29th minute.
Valeri then delivered a goal in first-half stoppage time and Danso produced his first of the season in the 47th minute -- giving the Timbers a four-goal overall advantage.
Seattle staged a late rally on goals from DeAndre Yedlin and Eddie Johnson, but the Sounders had dug themselves too big a hole from which to escape.
The Eastern Conference finals will begin on Saturday with Kansas City visiting Houston.