Kelce had 11 catches for 160 yards and a touchdown, and Hill took a handoff 70 yards for another score, as the Chiefs (11-4) beat the Broncos (8-7) for the third consecutive time and eliminated the Super Bowl champions from postseason contention.
Kansas City punctuated the win in style when 346-pound defensive tackle Dontari Poe, lined up at quarterback, threw a jump pass out of the wildcat formation to Demetrius Harris with less than two minutes left.
The Chiefs were already assured of a wild card when Pittsburgh beat Baltimore earlier in the day. But a win next weekend in San Diego coupled with an Oakland loss in Denver would give the Chiefs their first division title since 2010, not to mention a first-round bye and a home playoff game.
Meanwhile, the Broncos trudged through another inept offensive performance.
Trevor Siemian completed 17 of 43 passes for 183 yards and threw a game-ending interception. The only TD drive he led came after a pick gave the Broncos the ball at the Kansas City six-yard line. Justin Forsett scored two plays later.
The lackluster performance came one week after a dismal showing in a 16-3 loss to New England led to a locker room shouting match between the Denver offense and defense. The Broncos downplayed any kind of disharmony this week , but their performance on a sloppy, soggy Christmas night at Arrowhead Stadium only seemed to underscore the rift during a most frustrating of seasons.
Kansas City took control of the prime-time matchup from the opening bell.
Alex Smith capped a 77-yard touchdown march with a 10-yard keeper in the first quarter, and Hill out-ran the banged-up Broncos a few minutes later to give the Chiefs a 14-0 lead. It was the fourth TD scored by Hill against the Broncos this season.
Forsett's touchdown gave the Broncos fleeting hope, but it was dashed moments later. Kelce took a screen pass and followed perfectly executed blocking for an 80-yard touchdown and a 21-7 lead.
The Chiefs' defense took care of the rest to make it a festive night for their fans.