Kaepernick's rushing total was a record for a quarterback in a single NFL game, smashing Michael Vick's former mark of 173 set in 2002.
The Wisconsin native scored twice on the ground and completed 17-of-31 passes for 263 yards with a pair of touchdown tosses to Michael Crabtree as the 49ers reached the NFC Championship Game for a second straight year.
Crabtree finished nine receptions for 119 yards for second-seeded San Francisco, which now goes on to face the winner of Sunday's divisional round game between Atlanta and Seattle.
The Packers got a 26-of-39, 257-yard performance from Aaron Rodgers, but it wasn't enough as the NFC North champions were eliminated from the post-season.
Rodgers tossed for a pair of scores and intercepted once in the loss.