McCluster's 38-yard reception provided the game's only TD. He also ran for 61 yards on nine carries as the Chiefs (5-7) snapped a four-game losing skid.
Palko used good ball management skills, tossing for 157 yards, and the Chiefs defense sacked Bears quarterback Caleb Hanie seven times -- three by rookie Justin Houston -- in the victory.
The Bears (7-5) finished with just 181 total yards for the game, much of which they played without star running back Matt Forte, who exited in the first quarter with a right knee injury.
Hanie finished 11-of-24 through the air for 133 yards and was picked off three times.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys