SAN FRANCISCO — Spanning several generations, Duke Coach Mike Krzyzewski has molded four-year stalwarts and one-and-dones into championship teams, instilled some teams with a floor-slapping toughness and others with a freewheeling offense, and at times has seemed to be able to bend a referee’s whistle to his will.

Krzyzewski’s neatest trick, though, may be taking his final team — and his greenest — to another Final Four.

The Blue Devils, seeded second in the West region, kept alive their hopes of sending Krzyzewski into a retirement with a sixth national championship by turning back fourth-seeded Arkansas in the round of 8, 78-69.

As befitting a talented young team that is hitting its stride at the most opportune time, freshmen Paolo Banchero, who scored 16 points and Adrian Griffin, who had 18, spurred Duke. Center Mark Williams, a sophomore, added 12 points, 12 rebounds and 3 blocked shots.

The victory sends Duke to a Final Four for the 13th time under Krzyzewski — and the first since the Blue Devils won the title in 2015. Duke (32-6) will play either its fiercest rival, North Carolina, or the miracle makers from tiny St. Peter’s next Saturday in New Orleans.

As Duke dribbled out the final seconds, guard Wendell Moore wrapped an arm around his coach’s shoulder, and when the buzzer sounded the Blue Devils danced off the bench.

Krzyzewski tells his players that reaching the Final Four is like crossing a bridge, and on the other side is an entree into an exclusive brotherhood with the Blue Devils’ best teams. If Krzyzewski had plenty to be thankful for in his career, he acknowledged on the eve of facing Arkansas just how much one last trip would mean to him.

“You can only give so much to the church,” Krzyzewski, the son of Polish immigrants who grew up in Chicago, said with a laugh. “You want something back, you know? A little bit of forgiveness and less of a penance when you go in the box, you know? It would be a cool thing.”

While Duke had earned a high seed and had a roster again dotted with blue-chip prospects, this trip to the Final Four was hard to see coming when the tournament pairings were announced two weeks ago.

Krzyzewski, who called the Blue Devils performance “unacceptable” in a home loss to North Carolina in the regular-season finale, realized he had some work to do to repair the psyche of an exceptionally young team — the top six rotation players are 20, 20, 19, 18 and 18.

“I had a good meeting with myself,” said Krzyzewski, who emphasized the importance of a leader being his chief critic. “I said that I’ve got to do something. I’ve got to help in some way, and part of it was my approach with them.”

He added: “If you don’t put truth on the table and take responsibility, they you won’t make the best out of the situation that you are in.”

A team that looked fragile, even in advancing to the Atlantic Coast Conference tournament final, has gradually gained its footing in the N.C.A.A. tournament. It began with a comfortable win over Cal State Fullerton, and continued with late comebacks against Michigan State and Texas Tech, fueled by impeccable shot making. (The Blue Devils made their final five shots against Michigan State and their final eight against Texas Tech, the nation’s top defensive team.)

Over the last two weeks, Krzyzewski — who was shaped as an Army point guard by the unyielding Bob Knight — has given the air of a coach in tune with his team. He put point guard Jeremy Roach into the starting lineup for the first time in a month and he has been superb. He turned to a zone — which once would have been unthinkable — in the second half against Texas Tech, and then let his young players convince him to switch back to man-to-man in the final minute.

Krzyzewski even got down on a knee and slapped the floor late against Texas Tech — and his players followed suit, sending Duke fans here into a frenzy.

On Saturday night, with Roach being harassed by the Hogs defense, Krzyzewski turned early to Trevor Keels, who had been replaced by Roach in the starting lineup and played a season-low 14 minutes against Texas Tech. Keels, a freshman with a sturdy build, steadied Duke’s offense and delivered a 3-pointer at the halftime buzzer to push the lead to 45-33.

When the Razorbacks surged in the second half, narrowing the gap to 53-48, Krzyzewski called timeout to calm his team. He made sure the offense ran through his best player, Banchero, and signaled “1-2” from the sideline, instructing his defense to switch to zone. Banchero, who would be named the regional’s most outstanding player, scored in the post, passed to A.J. Griffin who drove for another basket and made two free throws and in a flash Duke had a working margin at 59-48.

Arkansas never threatened the rest of the way.

A year ago, Krzyzewski had left the impression that he had lost his iron grip on the program that he had become synonymous with: an N.B.A. prospect quit at midseason, he snapped at a reporter from the school newspaper, and his team missed the N.C.A.A. tournament for the first time in more than a quarter century.

No men’s coach has retired after winning a national championship since 1977 when Al McGuire, who was 48, retired after Marquette won the title. Two years earlier, John Wooden told his team after a semifinal victory over Louisville that he would retire following the title game, which the Bruins won against Kentucky.

Krzyzewski, 75, gave himself a much longer runway. He took the rare step last June of announcing his retirement effective at the end of this season. He said he did not want to go out the way he did last season, when Duke was 13-11 and saw its chances of making the N.C.A.A. tournament vanish when it had to drop out of the Atlantic Coast Conference tournament because of a coronavirus outbreak within the team.

The decision to announce it — and assistant Jon Scheyer as his replacement — was to avoid misleading recruits who might have asked how long he intended to coach, he said. Still, the whole season has been something of a last waltz tour.

“It wears on you a little bit because everywhere you walk, everyone is taking a picture of you, they’re watching everything,” Krzyzewski said earlier this week. “Look, that gets old.”

He added: “But I feel for my guys. They’ve had pressure on them that we’re not putting on them. I tell them all the time, we’re playing for us — for you — but then it just works out. No one — it’s not a sinister plan against us or anything, but it just happens that way.”

Duke won the A.C.C. regular-season title for the first time since 2010, but lost Krzyzewski’s final game at Cameron Indoor Stadium, against North Carolina — which soured the postgame celebration that included 96 former players — and were trounced again in the A.C.C. conference tournament championship game by Virginia Tech.

“All season we’ve been dealing with it,” Banchero said. “It’s coach’s last something every game.”

The two late-season losses wiped away any opportunity that Duke would be a top seed — or the chance that the Blue Devils would head to Krzyzewski’s hometown Chicago for the round of 16, as he had requested if they were a No. 1 seed.

Instead, Duke was slotted into the West region, which has been a graveyard for Krzyzewski’s teams.

The Blue Devils had been placed in the West six previous times and have yet to reach a regional final — even in 2011, when as a No. 1 seed they were tripped up by Arizona in the round of 16. In fact, Duke has never won an N.C.A.A. tournament game played out West, losing regional semifinals in Anaheim in 2016 to No. 1-seeded Oregon), 2011 to fifth-seeded Arizona and 2003 to second-seeded Kansas. The Blue Devils, who had a first-round bye in 1984 when the tournament included 48 teams, lost to sixth-seeded Washington in a second-round game in Pullman, Wash.

This trip, though, has been a stroll down memory lane.

Krzyzewski spent four six-week stints in the early 1970s living at the barracks at the Presidio, the former Army post that sits in the shadow of the Golden Gate Bridge, when he was playing for the All-Army team that competed in an international military competition.

His team practiced this week at the University of San Francisco, on the same court where he had practiced regularly 50 years ago. His players surprised him by knowing the answer to a pop quiz: who was the best player on the Dons back-to-back national championship teams in 1955 and ’56. (Answer: Bill Russell.)

“I was ready to dig in on them, but they knew it,” Krzyzewski said.

And when it came time to taking the court, the Blue Devils had all the answers, too.