There, they greeted him individually and invited him to Philadelphia next year for the Vatican-sponsored Eighth World Meeting of Families. The triennial event is expected bring hundreds of thousands of visitors to the city, and more than a million if Francis comes to say Mass.
"We were not at all disappointed," a broadly grinning Corbett said at a news conference behind the square afterward. "I think he was excited to see this delegation."
"I'm ecstatic," said Nutter, who had presented the pope with a brightly colored jersey from his high school alma mater, St. Joseph's Prep, along with an invitation signed by the school's entire junior class. The prep is run by Francis' religious order, the Jesuits.
Both men said several times they were "optimistic" that the pope will come to Philadelphia in September, 2015 for the five-day World Meeting, which traditionally concludes with a papal Mass.
But they said they had little more than the pope's noncommittal smiles and nods on which to base their optimism. Vatican officials say the pope normally does not announce international travel plans more than six months in advance.
Corbett has predicted the World Meeting could bring $100 million in tourist revenues to the region. On Monday he said he based that figure on the revenues that Democratic and Republican presidential nominating conventions generate.
Wednesday's audience was more than 18 months in the planning. It began soon after Pope Benedict XVI announced at the 2012 World Meeting in Milan that Philadelphia would be the host city for the next one.
With the assistance of the Archdiocese of Philadelphia, the event's local sponsor, Corbett and Nutter made preparations for a private audience with Benedict in Rome that November to invite him to Philadelphia. The Vatican canceled their audience just days before it was to happen, however, and two months later Benedict shocked the world by announcing he was retiring.
After Francis' election to succeed Benedict last March, the archdiocese again approached the Vatican about a private papal audience with local civic and church leaders to discuss the World Meeting.
They were invited to come in March, with the expectation they would meet Francis as a group at his simple residence at Domus Sanctae Marthae, a six-story apartment building adjacent to the basilica that also serves as a guesthouse for visiting bishops.
But on Monday, the day the Pennsylvania delegation arrived in Rome, Archbishop Charles J. Chaput was already cautioning that a private audience - if it happened at all - might be very brief. The pope's schedule was tight, said Chaput, who noted Francis is scheduled to meet President Obama on Thursday.
"He might just wave to us in a hall," Chaput said.
Around that same time, however, Corbett said in an interview he was anticipating about 45 minutes for the private audience, and said he hoped to use his time with Francis to invite him to see some of the good work the Catholic community in Philadelphia does for the city.
But late Tuesday night the delegation received word that their meeting would not be at the residence, but at the Wednesday public audience that popes have held for decades in St. Peter's Square, typically before tens of thousands of people.
With Corbett and his wife leading the way, the delegation formed a queue on the steps outside St. Peter's Basilica. Then each individual - some accompanied by a spouse - stepped forward to shake hands and chat briefly with the pope. Some also presented gifts before moving on. Corbett and Nutter had the most time, about a minute each.
"We had a private audience in front of 100,000 people," Corbett joked afterward.
"We came as joyful pilgrims and left ecstatic pilgrims," said his wife, Susan. The two presented Francis with handmade Pennsylvania tiles bearing the names of the four evangelists, along with a book about Philadelphia's celebrated outdoor murals.
"He's a very joyful man," said Nutter, who also presented the pope with the jerseys of the city's five major league sports teams. (Francis did not try one on.)
Contact David O'Reilly at firstname.lastname@example.org or #doreillyinq on Twitter.