Kansas City outscored the Rapids 4-0 in the two-game series that ended a five-match playoff losing streak. Prior to the meetings with Colorado, it had been seven years since Kansas City had scored more than one goal in a post-season game.
Kansas City will play Sunday in the semifinals against an opponent to be determined.
Collin came through on a header in the 28th minute off a cross from Graham Zusi, who also assisted on Sapong's goal in the 76th minute.
Goalkeeper Jimmy Nielsen extended Kansas City's shutout streak to 365 minutes dating to the final two games of the regular season.
Colorado, which defeated Columbus in the wild-card round to get a chance at Kansas City, struggled after losing striker Caleb Folan, right back Kosuke Kimura and center back Drew Moore to injuries in the first of the two games.