Phil Dawson booted a 33-yard field goal just inside the right upright on the last play of the game to give the 49ers the victory after driving from their own 20 in the last five minutes after the Packers tied it 20-20 with a field goal of their own.
The temperature at the start of the game was a frigid five degrees Fahrenheit (-15 C) and dropped as the contest wore on as many players and on-field officials wore balaclavas for warmth.
San Francisco quarterback Colin Kaepernick rescued the Niners on three different occasions with key runs that helped set up scores for the NFC wild card team, which earned a date in next week's divisional round against the Carolina Panthers.
"Colin Kaepernick, I think we can all agree, is a clutch performer," San Francisco coach Jim Harbaugh told reporters after the bruising victory.