The Rapids (15-6-10, 55 points) clinched a playoff spot in back-to-back seasons for the first time since 2010 (the year they won their lone MLS Cup title) and 2011. Colorado moved to within three points of conference front-runner Seattle and into a tie for second with Sporting Kansas City.
The Timbers (14-13-4, 46 points), while still in the thick of a multi-team battle for one of the final four playoff spots in the conference, lost their third consecutive match. Portland entered the match in fourth place in the conference and ended the night tied for fourth with the LA Galaxy, who tied FC Dallas. Minnesota is one point behind those teams, and Vancouver is two points behind them.
Badji scored for the second consecutive game and recorded his second goal of the season.
Rubio scored his fifth goal of the season and made a major impact on Colorado's attack in his return after sitting out the Rapids' previous match.
Rubio assisted on Badji's goal, feeding the ball ahead to Braian Galvan, who made a spectacular long cross in front of Portland's goal. Badji timed his jump perfectly and headed the ball past goalkeeper Steve Clark in the second minute of first-half stoppage time.
Rubio then found his own way onto the scoresheet with his own header off another well-timed cross from Galvan in the 63rd minute. It was Rubio's first goal since Aug. 21 and helped deflate Portland, which had mustered some early second-half momentum.
Rubio nearly added a third goal in the 69th minute when his header hit the far post off a long free kick.
The Rapids played without defender Keegan Rosenberry due to an ankle injury he suffered in their prior match against Seattle.
Portland finished with slight edges in possession (55.9 percent) and shots on goal (4-3).
But Colorado goalkeeper William Yarbrough, who entered the match tied for second in the league in clean sheets, recorded four saves and his 12th shutout of the season.