Evans put Seattle in front in the 28th minute as the Sounders dominated play in the first half, while Johnson scored in stoppage time to seal the win after goalkeeper Michael Gspurning was sent off in the 85th for handling the ball outside his own penalty area.
The Sounders will now face the top seed in the Western Conference, Portland Timbers, with the first leg of the two-legged series taking place in Seattle on Saturday, Nov. 2.
Rapids goalkeeper Clinton Irwin kept his side in the match early as he produced a pair of big stops in the first 10 minutes before Seattle's Adam Moffat had a shot blocked on the goal line by defender Drew Moor.
The breakthrough came in the 28th minute when a cross from Seattle's Leo Gonzalez was only cleared as far as Evans 17 yards from goal. The United States international took the ball down off his chest and fired a volley inside the far post.
Colorado was fortunate to only trail 1-0 at halftime, and the Sounders went close again in the 54th when a free kick from Marc Burch struck the crossbar.
There were only a few anxious moments for Seattle in the game, and they came from mistakes by Gspurning, who spilled two crosses that were ultimately cleared, while he lost track of his place on the field and picked up a loose ball just outside his own penalty area in the 85th minute, earning him a red card.
Marcus Hahnemann entered the game in place of Gspurning, but he wasn't called into action as the best chance for the Rapids was a header from Hendry Thomas which sailed narrowly over the crossbar.
Johnson then sealed the win despite his side playing down a man when he collected a pass inside the area, beat a defender and tucked the ball inside the near post.
10/31 00:51:16 ET