NEW ROCHELLE, N.Y. — Sunday was not unfolding as planned for the Iona College men’s basketball team. Visiting St. Peter’s was playing rough-and-tumble ball, which had landed Iona in foul trouble and out of sorts. The frustration was evident when Nelly Junior Joseph, a sophomore center for Iona, tussled fiercely enough over a held ball with St. Peter’s Hassan Drame that both players drew technical fouls in an incident that nearly precipitated a brawl.

And when Jaylen Murray banked in a long 3-pointer just before the halftime buzzer to put St. Peter’s ahead, it would have been easy for the Gaels to think — as they retreated to the locker room — that maybe it was not their day.

But moments of frustration, or resignation, did not linger. Iona cranked up its defense, sped up its offense and raced off with a comfortable 85-77 victory, ensuring that the only remaining drama in the Metro Atlantic Athletic Conference would be whether Iona (18-3, 10-0) could become the first team to finish unbeaten in league play since La Salle did it 32 years ago.

As the game ended, Iona Coach Rick Pitino was awarded the game ball for his 800th career college victory, though that total incorporates the 123 victories — including the 2012-13 season’s national championship — at Louisville that were wiped out by the N.C.A.A. after a scandal that centered on players and recruits being provided strippers and prostitutes.

He was then doused with water by his players in the Iona locker room.

In a serendipitous twist, Pitino’s milestone, albeit unofficial, came amid Louisville’s continuing dysfunction, which did not end with his firing in 2017. After one season with an interim coach, Louisville hired Chris Mack as Pitino’s replacement. Mack was suspended for six games at the start of the 2021-22 season when potential N.C.A.A. violations came to light from his recording of a conversation with a former assistant later accused of extorting the school. Mack left the program last week with a $4.8 million settlement.

“I have no animosity toward Louisville because all the people that got Tom Jurich left,” Pitino said, referring to his former athletic director who was pushed out with him. “One guy lost his company,” Pitino added, referring to John Schnatter, the Papa John’s founder who resigned as chairman and from the University of Louisville board of trustees after using a racial slur. “The other guy … ”

He quickly shifted gears, adding that he hoped Louisville would hire Kenny Payne, the former Louisville player and Kentucky assistant who is now on the Knicks’ coaching staff.

“I’m just hoping,” Pitino said. “I’m not endorsing him because that would probably be the killer for him.”

It was a little more than four years ago that Pitino was fired ignominiously, becoming the one head coach to lose his job in a federal corruption investigation that has otherwise cost only assistants their careers. The N.C.A.A. still has not resolved Louisville’s case from the Pitino era, but after being exiled to Greece — he coached parts of two seasons at Panathinaikos — Pitino returned just days after the World Health Organization declared the coronavirus a pandemic to accept the job at Iona.

Iona’s quaint campus in New Rochelle, N.Y., with its small brick buildings 20 miles north of Pitino’s home in Manhattan, is the type of place that coaching lifers imagine themselves landing in their final days. Rick Majerus often mused about ending his career at St. Mary’s, where he could coach in near seclusion — and yet not be too far from San Francisco’s restaurants and Napa’s vineyards.

“It doesn’t have the bells and whistles I had at Louisville and Kentucky, but none of that bothers me,” said Pitino, 69, adding that as long as a supportive administration remains in place, he will be content at Iona. He enjoys the bus rides to games — he’ll take his first flight to a conference game this weekend against Canisius and Niagara — and cherishes working with players and developing a team ethic.

“It’s an easy lifestyle — to coach kids that really care,” Pitino said. “We’re not worried about ‘Let’s get a N.I.L. [name, image and likeness] for $150,000.’ Nobody worries about that; you just worry about playing ball, getting better.”

That has always been a core tenet of Pitino’s teams.

They have rarely been populated by rafts of future N.B.A. stars — the Utah Jazz guard Donovan Mitchell was among the few exceptions at Louisville, with a few more at Kentucky. Rather, Pitino looks for high-upside prospects who have the desire to work at their craft.

This is what drew three transfers who are starters — the graduate guards Tyson Jolly (Southern Methodist) and Elijah Joiner (Tulsa) and junior forward Quinn Slazinski (Louisville) — to Iona after last season.

“I’d say it’s been a process,” Jolly, who started his college career at Baylor and is now at his fourth school, said with a smile. Pitino would get on him for picking up his dribble and making a pass after beating his man off the dribble. He was worried about dribbling into trouble, but Pitino wanted him to put further stress on the defense.

“I was fighting him — we were fighting him — early on when we got here because he was demanding so much and we don’t understand exactly what he wants,” said Jolly, who like his teammates cannot have his phone with him during team meals and other group activities, a rule that applied to the team’s summer trip to Greece. “But he’s coaching us to make us figure it out and then, once we get it, he’s going to be proud of us.”

Pitino will be proud of Dylan Van Eyck, a 6-foot-8 graduate student from the Netherlands, when he stops cheerleading and picks up his man on defense. (There is little else to quibble about with Van Eyck, a sixth man who adds whatever the Gaels need — rebounding, scoring, passing and shot blocking.)

Or Walter Clayton Jr., when he becomes a sophomore and learns the intricacies of a defensive scouting report. (Clayton, a freshman guard who was offered scholarships to play football at Florida, Nebraska and Tennessee, provides a physical presence off the bench.)

Or Osborn Shema, a 7-foot junior backup center, when he puts on another 20 pounds and stops being pushed around underneath the basket. (Shema provided 5 points, five rebounds, three assists, two blocks and a steal against St. Peter’s.)

But nothing will please Pitino more than when Joseph, a 6-foot-9 sophomore with impossibly long arms, realizes that among the many attributes he brings to the Gaels, running point is not one of them. On Sunday, Joseph found himself seated next to Pitino after dribbling against the St. Peter’s press and losing the ball right in front of the Iona bench.

It was, apparently, a repeat violation.

“I said, ‘OK, I’m either going to learn to speak Nigerian or you’re going to learn better English,’” Pitino said.

Joseph protested that nobody was open.

“OK, I’ll look at the film,” Pitino said he told him. “If it’s open, God forbid you. And he started laughing. I said, ‘No, it’s not funny.’”

But Pitino was smiling.

It was the gesture of a coach who expects that Joseph’s dribbling indiscretions, along with more of his team’s shortcomings, will be cleaned up in the next six weeks, by which time his teams are typically playing at their best.

As it is, the Gaels have built a sturdy foundation: Knocking off Alabama in November — they nearly upset the Crimson Tide in the N.C.A.A. tournament last March — and beating Liberty, which leads its division in the ASUN Conference, and Appalachian State, which leads the Sun Belt Conference. Their three defeats have been to Kansas, Belmont and Saint Louis.

But this is a group that seems to determined to do more than garner an invitation to the N.C.A.A. tournament. It is a team that — like its once peripatetic coach — insists it will be around for a while.