Cassel (17-of-31 passing, 196 yards) found Pope on a 2-yard scoring toss in the first quarter, providing the game's only touchdown, and Matt Prater booted a pair of field goals for Kansas City (8-4), who stayed atop the AFC West with the win.
The Chiefs sacked Denver quarterback Kyle Orton four times for 31 yards of losses and yielded only five first downs through the air.
Jamaal Charles picked up 116 yards on 21 carries for the victors.
Orton was held to a mere 9-of-28 passing as Denver (3-9) lost for the seventh time in eight games.
Knowshon Moreno amassed 161 yards on 23 carries for the Broncos.