Morris scored in the 56th minute on a pass from Nelson Haedo Valdez as the Sounders took the semi-final series 3-1 in aggregate scoring. The Sounders won the first game of the Western Conference final 2-1 on Tuesday and needed only a tie to move on.
Seattle will play Toronto or Montreal on December 10 for the league title.
Toronto hosts Montreal in the second leg of the Eastern final Wednesday. The Impact won the first leg 3-2 in Montreal.
"The whole group just figures out ways to win games. That is their biggest strength," said head coach Brian Schmetzer. "Each game is different. This was a game against a tough opponent and they found a way to win.
"It is the whole entire team effort that has brought us to this point."
The Rapids played without their number one goalie Tim Howard who suffered a bad groin injury while playing for the US National team. Howard had season-ending surgery on November 17.
Morris, who was named the league's rookie of the year earlier this month, scored early in the second half on a sliding chip over Howard's replacement Zac MacMath.
The ball deflected off a Rapid defender to Valdez who sent it on to Morris who was able to get past the Colorado defence.
MacMath failed to make a sliding stop as the goal gave Seattle a nearly insurmountable aggregate goal lead.
"Great ball from Valdez. I saw there was a little opening there and I just tried to get it over (MacMath)," said Morris.
"It is so great for the team to accomplish this. It is for our fans. They deserve it."
It was only the eighth goal Colorado gave up at home this season.
The Rapids controlled the play in the first half and created several scoring chances with the best coming in the 23rd minute from Kevin Doyle. He came down the left side but was unable to connect on a centring pass attempt to teammate Sebastien Le Toux.
Shkelzen Gashi set up a shot for Jermaine Jones in the 32nd minute and later had a free kick from just outside the box that was blocked.