The visitors relied on a dominant defence, which did not allow a touchdown after Green Bay scored on the first drive of the NFC divisional play-off.
Special teams stepped up for the 49ers with minutes left in the game as defensive end Jordan Willis burst through the middle to block the Packers’ Corey Bojorquez’s punt – the first blocked punt return in San Francisco play-off history – with the ball landing near rookie safety Talanoa Hufanga who ran six yards to score.
Place-kicker Robbie Gould added the extra point, which left the scores tied up as the 49ers mounted a final drive that ended with Gould’s 45-yard field goal taking his side ahead 13-10 as the clock wound down.
San Francisco will play the winner of Sunday’s match-up between the Tampa Bay Buccaneers and the Los Angeles Rams in next weekend’s NFC championship game.
The Bengals intercepted Titans quarterback Ryan Tannehill three times, while Cincinnati signal-caller Joe Burrow threw for 348 yards and rookie kicker Evan McPherson nailed a 52-yarder field goal for the victory.