Gore capped a seven-play, 82-yard drive with a 5-yard touchdown run the third quarter, pulling the 49ers within three points at 24-21, and later added a go-ahead, 9-yard score.
San Francisco had trailed 17-0 in the second quarter.
Gore finished with 90 yards on 21 carries and Colin Kaepernick went 16-of-21 for 233 passing yards and a TD toss for San Francisco, which gained a berth in Super Bowl XLVII.
Vernon Davis hauled down five passes for 106 yards and a score as the 49ers logged the third-biggest road comeback in NFL post-season history.
San Francisco will meet Baltimore in the Feb. 3 Super Bowl, marking its first appearance in the championship tilt since 1994.
The Ravens defeated New England in Sunday's AFC Championship Game.
Atlanta's Matt Ryan completed 30-of-42 passes for 396 yards and three touchdowns.
Julio Jones made 11 grabs for 182 with two scores and Roddy White added seven catches for 100 yards for the Falcons.