SAN FRANCISCO — Colin Kaepernick did the passing and running, and Aaron Rodgers couldn’t keep up.

Kaepernick outplayed the reigning NFL MVP and former Super Bowl champion in one sensational, record-setting playoff debut and led San Francisco right back to the NFC championship game.

Kaepernick ran for a quarterback playoff record 181 yards and two touchdowns and threw two scoring passes to Michael Crabtree in guiding the 49ers to a 45-31 win over the Green Bay Packers in an NFC divisional game Saturday night.

Next up for the Niners: a game Jan. 20 for a spot in the Super Bowl, against the winner of Sunday’s game between the Seattle Seahawks and Falcons at Atlanta.

“It feels good. We’re one step closer to where we want to be,” Kaepernick said. “I feel like I had a lot to prove. A lot of people doubted my ability to lead this team.”

And what a playoff debut it was by the second-year pro making just his eighth NFL start. No doubting Jim Harbaugh’s big midseason gamble switching quarterbacks now.

Rodgers never got in sync for the Packers (12-6), finishing 26 of 39 for 257 yards with two touchdowns.

Kaepernick ran for scores of 20 and 56 yards on the way to topping the rushing mark of 119 yards set by Michael Vick in 2005 against St. Louis. Crabtree caught TD passes of 12 and 20 yards in the second quarter and wound up with nine receptions and 119 yards for the Niners (12-4-1) in the NFC divisional matchup.

San Francisco had 579 total yards with 323 on the ground, scoring its third-most points in the franchise’s storied playoff history.

Frank Gore and Anthony Dixon each added 2-yard touchdown runs in the fourth quarter for the No. 2 seed NFC West champions, slim favorites on their home field in a rematch of Week 1. They added to their memorable night by setting a franchise postseason record for yards rushing, 119 of those by Gore to complement Kaepernick.

Rodgers, the former Cal star passed up by San Francisco with the No. 1 pick in the 2005 draft, never got going.

This is another early exit for the Packers, who lost in the divisional playoffs to the eventual Super Bowl champion New York Giants a year ago and were denied a chance to defend the title they won after the 2010 season.

Those Green Bay road stars of two years ago — they won three away from Lambeau Field on the way to the Super Bowl — didn’t have it this time against San Francisco’s stingy defense and a no-fear, second-year quarterback who would not be denied.

San Francisco advanced to back-to-back NFC title games for the first time since reaching three in a row following the 1992-94 seasons, with 1994 their last trip to the Super Bowl.

With the sellout crowd at Candlestick Park waving red flags reading “Quest for Six” — a sixth Super Bowl title, that is — Kaepernick did his part and then some to deliver in the first key step. Even after an early interception that gave Green Bay all the momentum in a hostile road stadium.

Kaepernick topped Vick’s mark with the 56-yard keeper on an option play in the third quarter. That gave Kaepernick 163 yards on 12 carries, also setting a 49ers franchise record for the postseason.

Kaepernick joined Jay Cutler in 2011 and Otto Graham in both 1954 and ’55 as the only players with two rushing and two passing touchdowns in a playoff game.

David Akers kicked a 36-yard field goal moments before halftime to give San Francisco a 24-21 lead at intermission after Green Bay tried to ice the struggling veteran by calling timeout before his kick.

Mason Crosby’s 31-yard field goal tied the game at 24 midway through the third quarter, then Kaepernick took over again. San Francisco’s defense handled the rest.

Kaepernick had 11 carries for 107 yards rushing by halftime.

The strong-armed Kaepernick brushed off the pick-six he tossed on the fourth play of the game, then took control with his pinpoint passing to his favorite go-to guy — Crabtree — and with his quick-burst ability out of the pocket.