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.
Avril Lavigne denies racism in 'Hello Kitty' music video
Jeb Bush 'thinking about running for president' in 2016