The home side just needed to win to secure their post-season berth and they were on their way after only four minutes when Darlington Nagbe picked himself up after being fouled 25 yards out to send a fine free kick over the wall and into the back of the net.
However, they sat back after the early breakthrough and were too complacent as Rapids equalised just nine minutes later, Dominique Badji's effort from the edge of the box deflecting in off Liam Ridgewell to restore parity.
Shortly after the half-hour mark Nagbe struck again to put his side back in front when he flicked a looping header into the top corner of Zac MacMath's goal from Lucas Melano's cross.
Jorge Villafana added a third after 62 minutes when he drilled in a left-footed shot from 15 yards, before top scorer Fanendo Adi met Dairon Asprilla's cross to convert his 16th goal of the season from close range to add some gloss to the scoreline.
Timbers were denied an automatic route straight into the Conference semi-finals, however, as Vancouver Whitecaps secured victory over Houston Dynamo.