SAN ANTONIO — Saturday’s round of 8 matchup between No. 2-seeded Villanova and No. 5-seeded Houston was reminiscent of the college basketball games played decades ago: Two dogged, rebound-devouring defensive behemoths scratching and clawing and barreling through defenders for tough-to-come by points.

One team, the lower seeded Cougars, had aspirations of a run toward its first national championship in program history, and carried the best roster it has had in years. The other, Villanova, has been looking to reposition itself as one of Division I’s most feared programs after a few dismal tournament seasons.

In the end, Coach Jay Wright’s Villanova team was too aggressive, too poised and too focused for Houston, which seemed ill-prepared to face an opponent it had so much in common with. And even though the Cougars made a big run in the second half to narrow what had seemed to be turning into a romp, the Wildcats never relinquished the lead and won, 50-44, to advance to the Final Four for the fourth time under Wright and the first time since 2018.

“It was like playing against our own selves,” said Caleb Daniels, Villanova’s redshirt-senior guard, after the game. “They were just as physical as we were. It was a little street fight every possession trying to get a rebound.”

With just over a minute left in the game, Jermaine Samuels, Villanova’s leading scorer, delivered a driving layup to give the Wildcats a 6-point lead, which had blunted Houston’s attempts to come back from 11 points down midway through the half. Houston’s defense, which had been suffocating during its second half run, forced a turnover but could not capitalize, and by the time Villanova’s star guard Collin Gillespie drained two late free throws, the Cougars’ chances were gone.

“It was right there,” Kelvin Sampson, Houston’s head coach, said afterward. “We needed a big shot. In a lot of close games this year, somebody stepped up.”

He added: “But we didn’t.”

Wright’s team, after an inconsistent regular season that saw it tumble out of the top-10 after being ranked as high as No. 4, seemed to be playing its best basketball when it needed to be. The Wildcats have now won nine straight games, including three wins in the Big East tournament for that conference title. They entered the N.C.A.A. tournament as the No. 2 seed in the South region and rolled past Delaware, Ohio State and Michigan to reach the round of 8.

Villanova won national championships in 2016 and 2018, with rosters brimming with future N.B.A. talent and elite guard play, which has been a driving force of Wright’s tenure.

Villanova’s 2016 team featured Mikal Bridges of the Phoenix Suns, Josh Hart of the Portland Trailblazers and Jalen Brunson of the Mavericks. In 2018, it was Donte DiVincenzo, who now plays for the Sacramento Kings, who lifted the Wildcats past Michigan for their third national title in program history.

Gillespie, a fifth-year senior who was the Big East player of the year, is the latest in a long line of game-changing guards looking to lead his team to another national championship. He led the Wildcats in points (15.9) and assists (3.3) this season while battling ankle injuries.

On Saturday, Houston mostly took Gillespie out of the game, allowing him to take just one shot in the first half.

“He didn’t have to prove that he could make the big shots,” Wright said. “He could get shots for his teammates, and that comes with humility. If you’re arrogant and you feel like you’ve got to show what you can do, then maybe you don’t make good decisions.”

Houston’s defense and ability to guzzle offensive rebounds had been an impenetrable combination in the tournament until Saturday evening.

The Cougars outmuscled and outmatched the University of Alabama at Birmingham, plus Illinois and Arizona, never having met an opponent fully prepared for their collection of strength, size and athleticism. Until running into Villanova.

The Wildcats controlled the matchup the way they often do: using long possessions to set up good looks and dictate the pace.

Villanova’s ability to neutralize Houston’s strengths helped the team outlast the Cougars, even as Houston pulled within 2 points as it attempted to come back. Houston feeds off its opponents’ mistakes, but Villanova is a disciplined team that limits them.

The Cougars, known for their ability to box out and create extra possessions on offense, could only pull in two offensive rebounds in the first half, and could not depend on their ability to create turnovers by attacking ball screens.

On offense, the Cougars were inconsistent, looking the worst they had all tournament.

“We had a lot of opportunities. They didn’t go in,” Sampson said. “That happens. I’m disappointed we lost. I felt this was a game we could win. Not should win, but could win. We had to earn it.”

But Villanova underperformed on offense as well. One of the best 3-point shooting teams in the nation, the Wildcats shot less than 30 percent from beyond the arc in the first 20 minutes, going into the half without a single point from Gillespie.

Samuels, who powered Villanova over Michigan in the round of 16, finished with 16 points and 10 rebounds.

Since taking down Michigan in 2018, Villanova had been knocked out of tournament by Purdue in 2019 and was defeated by Baylor, the 2021 champion, in the round of 16 last year.

Houston’s program had been dormant for years before Sampson’s arrival in 2014.

Yet against Villanova, that identity that he had built of being tough and hyperathletic, similar to the way the Cougars had played decades ago, wasn’t enough. A few missed shots and some lost rebounds kept Sampson’s team short of the Final Four it had wanted.

“Credit Villanova,” he said. “In a year where I don’t think there’s any great teams in college basketball, Villanova’s got as good a chance as anybody.”