49ers faithful take note, facing the Cowboys should make you nervous

And why not? The Niners had just won their 11th game in a row, vanquishing the rival Seahawks for the third time this season. Rookie quarterback Brock Purdy had aced his latest test, throwing for a career-best 332 yards and three touchdowns. The third-seeded Vikings, a team many suspected as a fraud, were likely headed to Levi’s for a beatdown.

It was a great time to be alive.

Snap back to reality, 49ers faithful . It turns out the Dallas Cowboys are coming to town, and your Sunday just got a lot more stressful.

The fifth-seeded Cowboys, as those who watched their Monday night mauling of Tom Brady and the Buccaneers can attest, are a very good team that appears to be peaking at the right time. They’re certainly more formidable than the Vikings, who got eliminated by the sixth-seeded Giants on Sunday.

Realistically, the Niners have faced only one opponent of the Cowboys’ caliber this season: the Kansas City Chiefs, who obliterated S.F. in an October game at Levi’s that feels like a lifetime ago.

Are the Niners strong enough to defeat the Cowboys at their best? Absolutely. Is it a lock?

Just keep telling yourselves that.

Real 49ers fans, or at least those who have either been alive a while or know their NFL history, would never take the Cowboys lightly. The scars are too gnarly — on both sides of the rivalry, for what it’s worth — to discount the possibility of another trauma.

The Niners were on the verge of reaching their first Super Bowl in the early ’70s, but the Tom Landry-coached Cowboys eliminated them from the playoffs in three consecutive seasons. The first two (1970 and ’71) were NFC Championship Game losses. The next year’s divisional-round defeat was particularly painful. Vic Washington returned the opening kickoff for a touchdown, sending the Candlestick crowd into a frenzy. The 49ers jumped out to a 21-3 lead and were up by 12 late in the fourth quarter until Roger Staubach, aided by an onside-kick recovery, broke hundreds of thousands of hearts with two touchdown passes in the final two minutes.

That was the same day as the Immaculate Reception, by the way — a day that shall live in Bay Area football infamy.

We all know about the 1981 NFC Championship Game at Candlestick, featuring The Catch, which launched one dynasty (the Niners would win four Super Bowls in the ’80s) and effectively ended another (though Landry’s Cowboys did make it back to the next season’s conference title game).

Those were the Niners’ glory days, to be sure. The early ’90s, however, featured another protracted Holy War with the self-anointed America’s Team. Dallas’ shocking upset victory in the ’92 NFC Championship Game at Candlestick, and its resounding triumph in the following year’s rematch at Texas Stadium, shook the Niners’ franchise to its core, creating an existential crisis. San Francisco subsequently loaded up, vanquished the two-time defending champions in the ’94 NFC title game at Candlestick and brought home its fifth and final Lombardi Trophy, as Steve Young morphed from “Not Joe” to first-ballot Hall of Famer.

None of it was easy. Much of it was very, very messy.

Imagine the head coach of one team (Jimmy Johnson) guaranteeing victory on the radio, three nights before a conference title game, declaring, “And you can put it in 3-inch headlines.” Imagine the other team’s head coach (George Seifert) responding, “Well, the man’s got balls, I’ll tell you that. I don’t know if they’re brass or papier-mâché. We’ll find out here pretty soon.” Picture pre-game fights. Envision Jerry Rice, at midfield, refusing to shake the hand of Staubach, the Cowboys’ honorary captain, before the coin toss.

All of that happened in January 1994. And those were just the broad strokes.

There’ve been other Niners-Cowboys brouhahas over the years, most notably during a September 2000 game at Texas Stadium, when then-Niners receiver Terrell Owens celebrated two touchdowns by striking a pose on the star logo at midfield, the latter provoking a melee.

Granted, none of that historical intrigue has any bearing on what will go down Sunday, other than to haunt each team’s fans with bad flashbacks.

However, many current Niners and Cowboys have fresh recollections of last year’s first-round playoff game between the teams at AT&T Stadium in Arlington, a 23-17 San Francisco victory that featured a surreal climax. The Cowboys, attempting to set up a last-gasp shot to the end zone, mismanaged the clock, with Dak Prescott unsuccessfully attempting to spike the ball after a quarterback draw.

In the aftermath, it was tempting to clown the Cowboys for another postseason flameout. Since 1996, when they won their third championship in four seasons by capturing Super Bowl XXX, Jerry Jones’ team has won just five playoff games and has not advanced beyond the divisional round.

Here’s the catch: These Cowboys are no joke. The fifth of those victories, Monday night’s 31-14 thrashing of the Bucs in Tampa, showcased a team that looks well-rounded, well-coached and highly motivated.

Prescott, now in his seventh season, played the game of his life, completing 25 of 33 passes for 305 yards, with four touchdowns and no interceptions. The Purdy fairy tale has been captivating, but Prescott is a serious dude capable of rolling into Levi’s and blowing the Niners’ house down.

The Cowboys also have a relentless group of pass rushers, led by second-year ubermenace Micah Parsons, who’ll make it harder for Purdy to extend plays. They’re the rare team that might have a shot at running the ball on the Niners’ top-ranked defense, and they’re coached by a seasoned pro in Mike McCarthy, who has some huge postseason conquests in his past. This could be the team that Jones, the organization’s 80-year-old owner and chief football decision-maker, has been dreaming of since the mid-’90s — his chance to scream “How ’Bout Them Cowboys?” on a podium for the first time in more than a quarter-century.

The only glaring weakness Dallas displayed Monday was at kicker as Brett Maher had one of the worst performances in the history of his position, missing four consecutive extra-point tries. Think Chuck Knoblauch meets Steve Sax meets David Duval, with a touch of Rick Ankiel. On Wednesday, the Cowboys signed Tristan Vizcaino to the practice squad, which might mean Maher won’t kick on Sunday. If Maher does take the field at Levi’s, he should be greeted by a standing ovation.

That would be one way for 49ers fans to release some of their pent-up anxiety, because those who are honest with themselves have been stressed out since Monday night.

They have their reasons. The Niners will face their toughest test in months. Their quarterback will be making his seventh career start, against a franchise that has inflicted so much pain on his scarlet-and-gold-wearing predecessors.

Like John Brodie, Joe Montana, Steve Young and Jimmy Garoppolo before him, Purdy is going to have to confront America’s Team.

It’s a rite of passage, but let’s be honest: You wish he were lining up against the Vikings.

Michael Silver is a columnist for The San Francisco Chronicle. Email: mike.silver@sfchronicle.com Twitter: @MikeSilver