Seattle played a man down after Michael Gspurning was handed a direct red card for a bad foul in the 85th minute and Colorado launched all the offense it could in an attempt to force overtime.
Johnson, however, stepped around a defender at the top of the penalty area and easily beat goalkeeper Clinton Irwin to ensure the victory.
Seattle advanced into the Western Conference semifinals, where it will meet Portland in a two-match, aggregate-goal series. The first leg of that series will be played in Seattle on Saturday and the second leg will be contested in Portland on Nov. 7.
Houston will face Montreal on Thursday in the Eastern Conference's knockout playoff game, the winner moving on to meet New York.
Brad Evans scored the first Seattle goal, sending a shot across the face of the goalmouth and into the left corner of the net in the 28th minute.
Swim Week Miami Beach 2014 [PHOTOS]