The 49ers are just one win away from the Super Bowl. They are back in the NFC Championship Game, for the 16th time as a franchise.

And, as you might know, No. 16 has been kind of a lucky number for this organization.

After a long, long wait for the postseason, Levi’s Stadium is getting broken-in pretty rapidly. On Jan. 19, the 49ers will host the winner of Sunday’s NFC divisional playoff between Green Bay and Seattle.

In Saturday’s game, with No. 16 Joe Montana as one of the honorary captains, the 49ers used the tools they’d been perfecting all season to eliminate the Minnesota Vikings, 27-10. A dominating defense, solid running game and efficient passing led to the first lopsided outcome of the playoffs, perhaps not surprising because the Vikings had a short week, a second consecutive road game and a cross-country trip.

This was the first 49ers playoff game outside the city limits of San Francisco. Maligned Levi’s has been blamed for the curse that has hung over the 49ers since leaving the city of their birth, and the building has been waiting six years for its home team to be worthy of hosting a game.

This team is worthy. And the stadium was worthy.

“The energy was unbelievable, the crowd was awesome,” said Joe Staley, playing in his first home playoff game since January 2013. “This whole season it’s kind of been building.

“Playing here, you always kind of wondered what it would be like with the energy that we had at Candlestick those last few years. It’s very very comparable. If not more.”

There was a new and festive feeling in Santa Clara. The Great America parking lot was rocking four hours before kickoff, with fans wearing jerseys of past greats as well as the current top-sellers: quarterback Jimmy Garoppolo, tight end George Kittle and defensive end Nick Bosa. Inside, the players seemed particularly amped going through their warmups. Jerry Rice posed for photos and chatted with NFL Commissioner Roger Goodell. Bryant Young joined Montana as honorary captain.

The 49ers, in their first playoff game in six years and just their fourth home playoff game since 2003, answered a lot of questions.

Garoppolo starting his first playoff game? Aside from one lousy pass that was intercepted in the second quarter, he was cool. He was physical, with a lead block that toppled Vikings linebacker Anthony Barr. He was ready for the big moment.

Kyle Shanahan coaching his first playoff game since the Super Bowl debacle against the Patriots, when he was Atlanta’s offensive coordinator? He dialed up a deceptive, run-centric game plan that put Minnesota immediately on its heels. His team, after a bye, was prepared, healthy and dialed in.

Bosa ready for his first NFL playoffs? The rookie was everywhere, rushing the quarterback, dropping into pass coverage, part of a defensive line that overwhelmed Kirk Cousins with six sacks. When Bosa had the wind knocked out of him after a sack early in the fourth quarter, the crowd started a deafening “Bosa, Bosa, Bosa” chant. After a moment — Shanahan joked that his young star was “milking it” — Bosa jumped to his feet and pumped his fists in response.

“That was a really cool moment,” said Bosa, who confessed to some nerves because his older brother Joey, the Los Angeles Chargers’ star defensive lineman, was — in a rare instance — on hand to watch him play.

And Levi’s in its debut as a home playoff venue? It was packed. It was loud. The building is finally starting to create memories of its own.

The 49ers didn’t take long to christen the stadium. The defense forced the Vikings to go three-and-out on the intial drive. Then Garoppolo marched his team down the field for a score in a little over four minutes to take a 7-0 lead. And set the tone in the game.

“It’s huge,” Shanahan said. “We didn’t play all last week. We had our home crowd. You could hear the fans in pregame warmups: The stadium was electric. It was different. Our defense holds them and we were able to get seven.”

Shanahan’s game plan sounds simple: Run the ball 30 times or more. If the 49ers could do that, they would control the game, allow their defense to dominate and make the Vikings one-dimensional. Mission accomplished: The 49ers ran 47 times while the Vikings had just 10 rushing attempts.

It was a matter of one team imposing its will. By the end of the game, the Vikings were tired and frustrated.

“Later in the game, they were starting to jaw at each other,” Bosa said. “We were bringing it on them. They had some frustration.”

The 49ers had a cool little bookend moment, though only a few of the players on the team realized it. Their last playoff game, in 2014, ended with an interception in the Seattle end zone by Richard Sherman. One of the key moments on Saturday was an interception by Sherman that led to a 49ers touchdown, giving the them a two-touchdown lead.

“In big games, I show up,” Sherman said. “Year in, year out.”

That was once a way to describe the 49ers. Year in and year out, big game after big game, they showed up in the playoffs and balled out. It’s been a while, but this team is reminiscent of some past 49ers teams.

Staley could see that when he got into the locker room.

“I was excited because guys were excited we won, but nobody was really celebrating,” Staley said. “We realize how special this team is and what we can do this year.

“Guys are really focused on moving on.”

The 49ers are moving on. To their 16th NFC Championship Game, to be played against a familiar opponent, whomever it might be.

One win away from the Super Bowl.

Ann Killion is a San Francisco Chronicle columnist. Email: akillion@sfchronicle.com Twitter: @annkillion