49ers pride themselves on toughness, but can they beat their toughest opponent in months?

SANTA CLARA — We’re about to find out if the 49ers are as tough as the image they project.

Their divisional playoff game Sunday against the Dallas Cowboys at Levi’s Stadium will serve as a referendum on whether they’re superior in terms of the hard-bitten persona that has been carefully cultivated by coach Kyle Shanahan and general manager John Lynch.

Being a bully got the 49ers all the way to the NFC Championship Game a year ago with a 10-7 team that isn’t as good as this year’s NFC West champions and No. 2 seed. That run started with a 23-17 road win against Dallas, a game the Cowboys haven’t erased from their memory.

Dallas fell behind 23-7 and couldn’t pull off a late rally even though 49ers quarterback Jimmy Garoppolo’s throwing shoulder was confetti by the third quarter. The Cowboys had 14 penalties for 89 yards and have spent a year hearing about how the 49ers weren’t necessarily better, but just tougher mentally and physically.

This year’s 49ers team is deeper and more versatile on both sides of the ball. And everything about the way they play screams physicality. The way the run the ball from scrimmage. The way their receivers run after the catch. The way those who aren’t carrying the ball are committed to blocking downfield. The way their defenders swarm tacklers to get everyone in the same frame of film.

All teams strive to be physical. The next time you hear a coach preaching finesse will be the first. Yet it’s especially intense where the 49ers are concerned as they’re scouted, analyzed and scrutinized by national and local voices.

Even with a rookie quarterback in Brock Purdy who’s started one playoff game and excelled for half of it, the 49ers have the reputation of being the team no one wants to play for their ability to impose their will.

In between giving Dallas its due Thursday as a worthy opponent, tight end George Kittle cut to the chase.

“We’re just going to play 49er football and that’s just run the ball,” Kittle said. “It doesn’t matter what the look is, we’re going to run the football. I think they’re going to do everything we can to stop that, and that should be their game plan.”

Run the ball, stop the run. Win one-on-one matchups. Beat the opponent to the punch. Control the time of possession. The 49ers did it so well that 15 of the 16 teams they played over the course of the season lost the following week. The only one that didn’t was Kansas City, which had a bye after beating the 49ers. (The Cardinals didn’t play anyone following the Niners’ 17th game, as they missed the playoffs.)

Shanahan and Lynch won’t come out and say it, but the belief is that happens because teams that face the 49ers are the worse for wear because of having absorbed a beating.

The other reason opponents lost the following week is because in a lot of cases, they simply weren’t very good. Counting the records of Seattle, Arizona and the Rams just once, the 49ers’ opponents were 101-136-1 this season, a .424 winning percentage. The 49ers played eight teams with 10 or more losses and just four with winning records.

Tight end George Kittle (85) looks for running room against Chiefs’ safety Jaylen Watson (35) in a 44-23 loss by the 49ers to Kansas City on Oct. 23. Shae Hammond/Bay Area News Group

So yes, the 49ers were the better, tougher team but against a pretty easy schedule. The Cowboys will be the best opponent since Oct. 23, when Patrick Mahomes and the Kansas City Chiefs came to town and beat the 49ers 44-23.

Christian McCaffrey had been a 49er for just two days at that point, and 11 consecutive wins against often suspect competition have followed. There’s something to be said for putting away inferior opponents, but it’s not what playoff football is about.

Within the last month, there have been instances where the 49ers, particularly on defense, didn’t look like a team that’s going to play Mike Tyson to the Cowboys’ Michael Spinks. Quarterback Dak Prescott is coming off a career game, they have a dynamic running back in Tony Pollard, a big, powerful offensive line, a dangerous wideout in CeeDee Lamb and a productive tight end in Dalton Schultz.

In a 37-34 overtime win over the Raiders in Las Vegas, first-time starter Jarrett Stidham hurt the 49ers with both his running and passing. Tight ends Darren Waller and Foster Moreau got free, as did Davante Adams.

Then in the wild-card win over Seattle, Kenneth Walker III rushed for 54 yards on 13 carries in the first half. The 49ers trailed 17-16 before breaking it open in the second half.

In both instances, defensive coordinator DeMeco Ryans said the play of his unit was “not representative of who we are.”

To hear Dallas edge rusher Micah Parsons tell it, the Cowboys won’t get lulled into a tough-guy contest at the expense of the desired end result.

“The biggest misconception is that you have to go out there and be different, that you have to go out there and try to out-physical a team, that you want to play their game,” Parsons told reporters. “Why play their game? Play your game. Let’s play Dallas football. That’s all we’ve got to do.”

On Friday, Shanahan took the time to give his players a history lesson on the Cowboys-49ers rivalry, including NFC Championship Games following the 1992, ’93 and ’94 seasons. Dallas won the first two title games and was generally considered the more physical team with Emmitt Smith, a huge offensive line, quarterback Troy Aikman, wide receiver Michael Irvin and a stifling defense.

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Besides signing Deion Sanders, the 49ers signed Ken Norton Jr., Rickey Jackson and Gary Plummer to toughen up for the inevitable Dallas title game following the 1994 season.

The 49ers were tougher too, but that’s not why they won. They won because the Cowboys turned the ball over three times in the first four and a half minutes including a pick-six from Eric Davis and the 49ers got off to a 21-0 lead, eventually winning 38-28 en route to their last Super Bowl championship.

The 49ers won not because they were tougher, but because they played a cleaner game with fewer mistakes. If they don’t do the same thing Sunday, all the toughness and physicality will be lost amid the despair of a home playoff loss.