Larrys Mabiala struck in the final seconds of regulation time as the visitor broke the host's hearts at Dick's Sporting Goods Park.
The Timbers will play either Sporting Kansas City or Real Salt Lake in the Western showpiece after inflicting a first home defeat in 17 on the Rapids – and eighth defeat in nine play-off games.
Although, Giovanni Savarese's side ended the contest with 10 men as Dairon Asprilla was dismissed after appearing to strike Braian Galvan in the face.
The Rapids were unbeaten in their last five meetings with the Timbers and carried the greater first-half threat with nine attempts, three of which were on target.
Steve Clark twice came to the visitor's rescue. First, he made a smart save to keep out Mark-Anthony Kaye following a fine individual run, before denying the in-form Dominique Badji’s header from point-blank range.
The Timbers' struggles continued when a distraught Sebastian Blanco – the scorer of five goals in three games – was forced off injured within seven minutes of the restart.
Nevertheless, they worked their way into the contest and went close to breaking the deadlock when Jose Van Rankin's goalbound shot was cleared off the line by Danny Wilson.
And the 2015 MLS Cup winners snatched a dramatic victory with seconds of regulation time remaining, as Mabiala reacted quickest to volley home after a corner ricocheted kindly into his path.
Although, they were made to see out the dying moments with 10 men, when Asprilla was given his marching orders for violent conduct.