Kyle Orton, who was released by the Broncos earlier in the season, went 15-of-29 through the air for 180 and didn't throw an interception for the Chiefs (7-9).
Kansas City got the game's only touchdown on McCluster's 21-yard scamper in the first quarter.
Tim Tebow was limited to a mere 60 passing yards on 6-of-22 efficiency, but the Broncos (8-8) won the AFC West nonetheless after Oakland fell to San Diego Sunday.
Tebow couldn't find another miracle comeback and the Broncos now take a three-game losing streak into the post-season.
Celebrity Breakups and divorces of 2014 [PHOTOS]