The Cowboys took a 7-0 lead on Kansas City in the first quarter with a 6-yard touchdown pass from Dak Prescott to Cole Beasley.
Prescott completed 7 of 10 passes for 76 yards and the touchdown in the first quarter. Terrance Williams caught three passes for 43 yards, and Dez Bryant had two catches for 22 yards.
Ezekiel Elliott, who received an administrative stay on Friday that allowed him to play today, rushed for 23 yards on six carries in the first quarter.
The Chiefs gained only 38 yards on 10 plays in the first quarter, with Alex Smith going 4-for-5 for 20 yards and Kareem Hunt rushing for only 6 yards on four carries.