ATLANTA — The Falcons are well aware of just how desperate this city is for its first Super Bowl championship.
Mike Peterson sees and hears it everywhere he goes.
‘‘The city is hungry,’’ the Atlanta linebacker said. ‘‘You can feel it when you’re in the grocery store. Everybody is saying, ‘Go Falcons.’ Everyone is wearing red and black. The city is painted red and black.’’
The Falcons will be playing in the NFC Championship game for only the third time when they host the San Francisco 49ers Sunday, a matchup of teams that come into this game from very different historical perspectives.
For the 49ers, this is a chance to rekindle the franchise’s glorious legacy, to follow in the footsteps of those magnificent teams that captured five Super Bowls titles in the 1980s and ’90s, led by giants of the game such as Joe Montana, Jerry Rice, and Steve Young.
The Falcons? They’ve never won a Super Bowl. Heck, they’ve only gotten that far one time, during the 1998 season when a charismatic bunch known as the ‘‘Dirty Birds’’ shockingly made a run to the big game — and was promptly blown out by the Broncos in John Elway’s finale.
‘‘They’re trying to recapture greatness,’’ Falcons safety Thomas DeCoud said. ‘‘We’re trying to break the ceiling on it.’’
Although the Falcons (14-3) are the NFC’s top seed and playing at home, they opened as a 3-point underdog against the 49ers (12-4-1), who looked unstoppable in last week’s rout of the Packers in the divisional round.
The most dynamic player on that field was a quarterback who began the season as a backup. Colin Kaepernick took over the starting job when Alex Smith was injured, and coach Jim Harbaugh made the bold decision to keep it that way, even when Smith healed. Never mind that the former starter had led San Francisco to the NFC title game a year ago and was one of the top-rated passers in the league this season.
Harbaugh looked like a genius when Kaepernick ran all over the Packers in a 45-31 victory, turning in one of the great performances in playoff history.
It wasn’t so much that he passed for 263 yards and two touchdowns. What really stood out was what he did when he kept the ball himself. Kaepernick scored two touchdowns — including a 56-yarder in which he looked more like Michael Johnson than a football player — and finished with 181 yards rushing, a postseason record for a quarterback.
He also showed plenty of flare, celebrating his scores by flexing his right arm and kissing his biceps — a move that quickly became a social media sensation known as Kaepernicking.
‘‘He’s super fast, athletic and he can throw the ball,’’ 49ers running back LaMichael James said. ‘‘But once he takes off, he’s faster than a lot of running backs and linebackers. He’s an incredible athlete.’’
While certainly aware of their team’s proud background, most of these San Francisco players were molded by adversity. The 49ers went eight straight seasons without a winning record or trip to the playoffs until Harbaugh arrived in 2011 from nearby Stanford and immediately turned things around.
The team went 13-3, won the NFC West and advanced to the conference championship, where a fumbled punt return in overtime led to a wrenching 20-17 loss to the New York Giants.
San Francisco doesn’t want another chance to get away.
‘‘This opportunity is rare,’’ linebacker Patrick Willis said. ‘‘It doesn’t come that often even if we were here last year. The [eight] years before that we were at home and didn’t make the playoffs. Just to have that opportunity again to be here is one of those things we don’t take for granted.’’
Defensive end Justin Smith noticed a divergent mind-set after the victory over the Packers, compared to what he felt a year earlier, when the 49ers pulled out a last-second win on the Saints in the divisional playoffs.
‘‘We were so excited after winning the Saints game,’’ Smith said. ‘‘This was, ‘All right, we took care of business, find out who we play, it’s Atlanta, let’s go down there and take care of business and try to get to the big one.’ It definitely had a different feeling than last year.’’
The Falcons are coming off their first playoff win since the 2004 season, erasing a major stumbling block with their 30-28 victory over the Seattle Seahawks. It wasn’t nearly as easy as the 49ers’ victory.
After squandering a 20-point lead in what would’ve been the greatest fourth-quarter collapse ever in the playoffs, Matt Ryan brought Atlanta back in the final 30 seconds. Living up to his nickname ‘‘Matty Ice,’’ the fifth-year quarterback completed two long passes to set up Matt Bryant’s 49-yard field goal with eight seconds left.
After going one-and-done in his first three trips to the playoffs, Ryan is finally a postseason winner.
A burden has been lifted, for sure.
‘‘It’s a good thing to get that first win out of the way,’’ he said. ‘‘I think that everyone did a great job of not letting it distract us, but it can be distracting.’’
Now, to get started on a playoff winning streak.
‘‘I feel the same as I did last week,’’ Ryan insisted. ‘‘When you walk in and you turn on the film on a Monday or a Tuesday and you’re getting ready to play your next game, there’s a whole new laundry list of problems that you need to address. That’s more of where my focus has been, and I think that’s where it needs to be.’’
While Kaepernick is just getting started on what looks to be a hugely promising career, Tony Gonzalez is winding things down.
The Atlanta tight end is already assured of a spot in Canton, having caught more passes than anyone in NFL history except Rice, and revolutionized his often-obscure position. Despite a huge season in which he led the Falcons in catches, the 36-year-old has repeatedly said he’s 95 percent sure this will be his final year.
Like Ryan, he erased the one big blotch on his record by winning his first playoff game last weekend, making the final catch to set up Bryant’s winning kick.
But Gonzalez would really like to go out with a ring. Two wins to go.
‘‘That’s the goal,’’ he said. ‘‘Win a championship and get out of here.’’
Kaepernick’s performance against the Packers was so impressive that San Francisco actually became a bigger favorite during the week, at least according to the oddsmakers, who said Atlanta was the biggest underdog of any top-seeded team playing at home since the playoffs expanded in 1978.
The Falcons are comfortable with that role. All season long, they’ve been criticized for failing to win games impressively, even at the Georgia Dome, struggling mightily to beat lightweights such as Oakland, Arizona, and Carolina.
‘‘We’ve had that chip on our shoulder from Day One,’’ Peterson said. ‘‘But I don’t think me or anybody in this locker room has a problem with playing the underdog role, playing the team that everybody’s doubting. We’ve been that every week.’’