James Morrison and Somen Tchoyi also scored for Werst Brom while Peter Lowry and Eddie Johnson scored for the Timbers, who gave many of their regular starters the night off.
Johnson put Portland ahead just before the half hour with an angled shot from the right that sailed past goalkeeper Boaz Myhill. Portland scored again three minutes later through Lowry's strike from outside the box.
Bullet: Gabriel Tamas (right) earned victory for West Brom with a stunning late strike
Morrison fluffed a chance tor reduce his side's arrears when he missed a penalty in the 63rd minute, but made no mistake minutes later, firing past goalkeeper Jake Gleeson to make it 2-1.
Tchoyi equalised in the 68th minute before West Brom pushed for a third in the final 10 minutes, but were unable to score until Tamas' memorable goal from 30 yards with just seconds left.
Comeback: James Morrison (right) got West Brom back into the match despite missing a penalty
'You see one of those strikes once in a blue moon, and today was a blue moon day for us,' manager Roy Hodgson said.
West Brom began their tour of the U.S. West Coast with a 2-1 defeat to the San Jose Earthquakes, but bounced back to beat Ventura County Fusion 4-2 on Sunday.
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