Jean-Baptise worked his way into the box to get his head on a Diego Valeri corner kick just before the final whistle, triggering an emotional celebration at Jeld-Wen Field as the Timbers (8-2-9) grabbed possession of second place in the Western Conference.
Ryan Johnson scored in the 27th minute for Portland.
Marcelo Sarvas scored in the 17th minute for the Galaxy (9-8-3), who fell to fourth place in the West.
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