The Eagles took a 24-0 lead into the fourth quarter, with Vick throwing for 98 yards and scoring on an 8-yard run in the second period. Young came on in the second half and scored from 10 yards out in the third period.
Philadelphia's two quarterbacks combined to throw 30 times without an interception.
Cleveland's Colt McCoy, who had put in two excellent starts to open the pre-season, was 9-of-18 for 89 yards and an interception. Both of the Cleveland touchdowns came with Seneca Wallace at quarterback.
Philadelphia has won two of its three exhibition games. Cleveland is 1-2.