Vick's late, 4-yard scoring pass following a 16-play, 91-yard drive redeemed a season-opening performance in which he tossed four interceptions.
He finished with 317 yards on 29-of-56 passing efficiency while LeSean McCoy contributed 110 yards on 20 carries, but lost a fumble.
Philadelphia (1-0) sealed the victory with its fourth interception of the day off rookie Browns quarterback Brandon Weeden.
Weeden went 12-of-35 through the air for 118 yards in his debut for the Browns (0-1).
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged