The Eagles remained unbeaten in three exhibition games.
Vick suffered a rib injury in the Eagles' second preseason tilt and Foles stepped in to guide Philadelphia to a 17-3 halftime lead.
Foles completed 12-of-19 passes and had first-period scoring throws of 7 yards to Brent Celek and 2 yards to Dion Lewis.
Trent Edwards came on in the second half and threw a 4-yard touchdown pass to Brett Brackett.
Cleveland's Brandon Weeden, the 22nd pick in this year's draft, was 9-of-20 for 117 yards with three sacks and a lost fumble.
Philadelphia and Cleveland will face each other to start the regular season Sept. 9. The Browns suffered their first loss in three exhibition contests.