The 49ers advanced to the NFL championship game for the first time since 1995.
They will face Baltimore, who defeated New England 28-13 in Massachusetts on Monday (EDT), in the Super Bowl in New Orleans on February 3.
San Francisco, who lost to the Super Bowl champion New York Giants in the NFC title game last year, will be playing in their sixth Super Bowl in franchise history.
The 49ers are a perfect 5-0 in the championship game and will be trying to join Pittsburgh as the only clubs with a half dozen Super Bowl triumphs.
The top-seeded Falcons were hosting their first NFC championship game on Sunday but they couldn't get the job done against dynamic quarterback Colin Kaepernick and the 49ers.
San Francisco trailed 17-0 midway through the second quarter before charging from behind in the second half as their offence came to life.
Gore romped nine yards for a touchdown to put San Francisco ahead 28-24 with 8:23 left. After that it was up to the defence to do their part.
Atlanta's Harry Douglas made an acrobatic 22-yard catch to put the ball on San Francisco's 28.
The Falcons advanced the ball to the 10-yard line, setting the stage for the contest to be decided on two plays.
On third-and-four, Ahmad Brooks broke up quarterback Matt Ryan's pass and NaVorro Bowman got the ball back for the 49ers after knocking down Ryan's toss to Roddy White on the fourth down.
"That was a great finish for our defence," San Francisco coach Jim Harbaugh said.
"It put an exclamation point on the game."
San Francisco ran down the clock with their next possession before Atlanta got the ball back on their own 41 yard line with six seconds to play. Julio Jones caught a 24-yard pass on the final play of the game.
"We moved the ball effectively the entire day," Ryan said.
"We had two chances where we were in positive territory and didn't walk away with points.
"When you do that against a very good football team you're not going to win."
It marked the 49ers' first playoff road win in 24 years and just the third in club history. Their last post-season road win came in 1989 against the Chicago Bears.