Gore found the end zone on a 4-yard run in the first quarter to open the scoring and the 49ers never trailed.
Alex Smith went 15-for-24 through the air for 177 yards and connected with Michael Crabtree on a 2-yard TD pass in the second quarter for San Francisco, which won a fifth consecutive game for the first time since 2001.
David Akers booted a pair of field goals in the victory.
Colt McCoy picked up 241 aerial yards on 22-of-34 efficiency with a touchdown and an interception for the Browns (3-4).
Celebrity Couples of 2014 [PHOTOS]