Goalkeeper William Yarbrough posted the shutout for the Rapids (7-6-4, 25 points, 1.47 points per game), who won at Providence Park for the first time since 2011.
The Timbers (11-6-5, 38 points, 1.73 points per game) dropped out of first place in the Western Conference after failing to put any of their 11 shot attempts on frame. They came close to getting the equalizer in second-half stoppage time, but Dairon Asprilla's 5-yard shot banged off the outside of the left post.
MLS last week announced that playoff seeds would be determined by points per game, largely because the Rapids had five games postponed this season due to COVID-19 issues.
Since then, the Rapids have come alive, dominating the Seattle Sounders 3-1, and controlling the Timbers to reach the playoffs for the first time since 2016.
Acosta, who was making his first appearance since Sept. 23, entered as a substitute in the 58th minute and scored his second goal of the season and his first since the MLS is Back Tournament in July.
The goal came after a Portland turnover near midfield. Colorado's Diego Rubio stole a pass and worked a nifty give-and-go with teammate Younas Namli before dribbling the ball to the top of the penalty area.
Rubio sent a pass to Acosta on the left wing, from where the ninth-year veteran made a quick move to get past a defender before putting a 15-yard shot into the upper right corner of the net, leaving Timbers goalie Steve Clark no chance.
Clark made three saves.
The Rapids, the lone MLS team that hasn't been awarded a penalty kick this season, appeared to have their first chance in the 15th minute when a ball went off Portland defender Bill Tuiloma's foot and up off his arm in the 18-yard box. Referee Joseph Dickerson originally pointed to the penalty spot, but rescinded the call after a video review.
The Timbers played without forward Jaroslaw Niezgoda, who suffered a torn anterior cruciate ligament in his left knee Sunday and will miss the rest of the season.