Kaepernick completed 15-of-28 passes for 196 yards with a 1-yard TD toss to Vernon Davis and carried the ball eight times for 15 yards with a 4-yard scoring run as the 49ers gained the NFC title game for a third straight year.
Kaepernick improved to 4-1 in his post-season career with San Francisco, which will face Seattle on the road next week for the chance to represent the NFC in Super Bowl XLVIII.
The 49ers clamped down on defense in the second half, holding Carolina scoreless after the break. They sacked Panthers quarterback Cam Newton four times and recorded a pair of interceptions.
Newton finished 16-for-25 through the air for 267 yards with a score and ran for 54 yards on 10 carries as Carolina fell in its first playoff game following a 12-4 regular season.
Ted Ginn made four grabs for 104 yards.