Gore's 12-yard scoring run with 3 minutes left handed San Francisco (3-1) its first lead and completed a comeback from a 20-point deficit midway through the third quarter.
The 49ers' halfback finished with 127 yards on 15 carries while Alex Smith completed 21-of-33 passes for 291 yards and a pair of scores in the victory.
The Eagles (1-3), meanwhile, were shut out in the fourth quarter and coughed up a late lead for the third week in a row.
Michael Vick hurled for 416 yards on 30-of-46 passing efficiency with two touchdowns and an interception in the loss.
DeSean Jackson was his favorite target, making six grabs for 171 yards.