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Vernon Davis caught a touchdown pass in the fourth quarter to put San Francisco in front. Reuters

The San Francisco 49ers beat the Packers 23-20 on a last-second field goal to win a fierce battle in brutally cold conditions at Lambeau Field in Green Bay, Wisconsin in their wild card round playoff game on Sunday.

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.

Twice the Packers took the lead from the 49ers, once in the second quarter and again in the fourth quarter, but both times San Francisco responded on their next possession with touchdown drives keyed by long runs by Kaepernick.

The long-striding Wisconsin native dashed 42 yards to help put the Niners back in front 13-7 in the first half, and after they fell back 17-13, ripped off a 24-yard run to set up another score for a 20-17 lead.

After Green Bay tied the score 20-20 on a 24-yard field goal by Mason Crosby with 5:06 left, Kaepernick did it again.

On a third-and-eight from the Green Bay 38-yard line, just outside field goal range in the Arctic conditions, Kaepernick rolled left to get away from the pass rush and gained 11 yards to keep the drive alive and move the ball into field goal range.

Running back Frank Gore did the rest, powering through the middle to move the ball closer and set up a comfortable kick for Dawson.

Kaepernick, who played sleeveless though he did wear a balaclava under his helmet, completed 16 of 30 passes for 227 yards, one touchdown and one interception. He ran the ball seven times for 98 yards.

"It's not that cold," Kaepernick told a TV interviewer on the field after the triumph. "It's all mental."

Green Bay quarterback Aaron Rodgers, after a quiet first quarter, finished up hitting 17 of 26 passes for 177 yards and a touchdown. Rookie running back Eddie Lacy ran like a battering ram, gaining 81 yards on 21 carries.

"We were one play away," said Packers coach Mike McCarthy. "One play not good enough."

(Reporting by Larry Fine in New York, Editing by Gene Cherry)