MLS announced last week that qualification for the playoffs would be determined by points per match, as Colorado had five games postponed because of the COVID-19 pandemic.
Shinyashiki opened the scoring in the 11th minute, taking a cross from Sam Vines and putting a header from 10 yards out just inside the right post. Nicolas Benezet also was credited with an assist.
Morris tied it in the 22nd minute, redirecting a cross from Cristian Roldan into the net from close range.
Rosenberry made it 2-1 in the 42nd minute. A Colorado corner kick was headed away by Sounders defender Yeimar Gomez Andrade, but the ball fell to Rosenberry, who was about 23 yards out in the middle of the field. His low volley made it through a maze of players and just inside the left post.
The defending MLS Cup champion Sounders nearly tied it in first-half stoppage time, but Colorado goalkeeper William Yarbrough made a left-footed kick save at the near post on a 5-yard shot by Raul Ruidiaz.
Bassett extended the Rapids' lead to 3-1 in the 75th minute, scoring on a header from 7 yards out off a free kick from Jack Price.
Yarbrough made two saves for Colorado, and Sounders goalie Stefan Frei stopped seven shots. Colorado outshot Seattle 16-9, including 10-3 in attempts on target.