Kaepernick was also 17-of-31 passing for 263 yards and two touchdowns, but his ability to run the ball created opportunities for the San Francisco offense that amassed 581 yards in the game.
With the win, the 49ers advanced to the NFC title game for the second consecutive year. San Francisco will either host Seattle or play at Atlanta next weekend depending on the outcome of Sunday's game between the Falcons and Seahawks.
The Packers led 14-7 after the first quarter but fell behind by three, 24-21, at halftime. The 49ers outscored the Packers 21-10 in the second half to secure the 14-point win.
Aaron Rodgers was 26-39 passing for 257 yards and two touchdowns in the loss.