The Bears had a 28-10 advantage heading into the fourth quarter and went on to finish the preseason with a 3-1 mark.
Chicago quarterback Jay Cutler did not play Thursday and McCown turned in a solid performance by completing 20-of-29. He hit Dane Sanzenbacher with a 30-yard scoring pass in the first period and found Armando Allen with an 11-yard touchdown throw in the second.
The Bears also scored on the second half on a 15-yard interception return by Greg McCoy and a 22-yard blocked punt return by Brittan Golden.
Colt McCoy, last year's Cleveland starter, went 2-of-5 for 16 yards and an interception. Rookie Brandon Weeden was held out of action.
Cleveland (2-2) will host Philadelphia to start the season while Chicago will be at home against Indianapolis.