Jefferson Savarino scored in the 87th minute to deny the Timbers' comeback attempt.
RSL blitzed the opposition in the first half, outshooting the visitors 9-0. Damir Kreilach found a breakthrough in the 28th minute when he drifted into the box to head in an uncontested cross.
Portland goalkeeper Steve Clarke produced a string of spectacular saves to limit the damage.
When the teams broke for half time, it appeared RSL would run away with the match. However, the ensuing 45 minutes went far off-script.
The Timbers hit their opponent immediately and, as was common in the first round of the 2019 playoffs, found an equalizer off a corner kick. Dairon Asprilla leaped over several defenders to galvanize Portland.
The hosts stabilized themselves and Savarino soon found himself in open space to decide the contest.
Freddy Juarez's side will now travel to Seattle to face the Sounders on Wednesday.