Patricia Brett stayed up the entire night, fortifying herself with coffee.

At 4:30 a.m. Sunday (Boston time), Pope Francis would officially declare Mother Teresa a saint and Brett wanted to be awake for every second of it.

“There was no way I was going to miss the canonization,’’ she said. “I wanted to be in the moment.’’

Brett was one of many Catholics who woke up before dawn to watch the event broadcast live from Vatican City. Too excited to go back to sleep, several of them filed into the newly named St. Teresa of Calcutta Church in Dorchester 4½ hours later to hear Cardinal Seán O’Malley preside over the Mass celebrating the canonization of the Albanian-born nun.

Thousands of pilgrims gathered in St. Peter’s Square to hear Pope Francis’s declaration. O’Malley was supposed to leave Friday for Italy to attend the ceremony but a death in his family kept him in Massachusetts.

In his homily, O’Malley recalled the first time he saw Mother Teresa — it was in the 1960s at Catholic University in Washington D.C., where O’Malley was teaching. She was not famous yet and only about 20 people appeared at a ceremony to honor the work she was doing with the Missionaries of Charity, the order she founded in 1950.

O’Malley was overwhelmed by the stories he heard about the nun. He recalled how Eileen Egan, a journalist and peace activist with Catholic Relief Services, described her visit to India, where she saw a dying man, covered in maggots, being carried in a wheelbarrow through the streets. It looked like the wheelbarrow was moving by itself until Egan spotted a tiny woman pushing it. Mother Teresa was taking him to a Hindu temple where a makeshift hospice had been built to let people die in dignity, O’Malley said.

“She brought hope and comfort to so many who were in pain and despair,’’ O’Malley said. “Our tendency is to be nice to someone only when they are nice to us first . . . Jesus says don’t wait for someone else to take the first step. That’s the way Mother Teresa was. She loved first.’’

Three nuns from the Missionaries of Charity sat at the front of the church, dressed in the blue and white saris that became the habits of the order that Mother Teresa founded. After the Mass in Dorchester, O’Malley said, they would be heading down to New Bedford for another celebration Mass.

“It’s going to be party, party, party all day,’’ O’Malley joked.

At the end of the Mass, he presented them with a small, bronze replica of the famous sculpture “Homeless Jesus,’’ by Timothy Schmalz, which shows a man shrouded in blankets, lying on a bench. His face is hidden but he is revealed as Christ through the wounds on his feet marking where he was nailed to the cross.

The gesture was a callback to a gospel passage in Matthew, read during the Mass, which warns that those who ignore the neediest, ignore Christ himself.

Mother Teresa visited Massachusetts several times, most recently in 1995, two years before she died.

Patricia Brett recalled meeting her twice, the first time in 1988, when the nun came to Massachusetts and visited MCI-Concord, a medium-security prison. Brett and her husband, then-state representative Jim Brett, remembered how moved the inmates were to see her, some to the point of tears.

A correctional officer approached Jim Brett and told him he had seen other religious leaders, like Jesse Jackson, visit the prison. No one had the same effect on the inmates that Mother Teresa had, Jim Brett said. He recalled the officer telling him: “ ‘I’m not a believer. But she’s special.’ ’’

O’Malley said the sainthood of Mother Teresa, who died at 87, is inspiring to Catholics around the world, who remember her work with the poor and those stricken with AIDS, leprosy, and tuberculosis.

“Holiness isn’t just something that is in the past,’’ O’Malley said in an interview after the Mass. Her canonization “is a great sign of encouragement. All of us know the work of saints who lived in faraway places centuries ago. Here is a woman from our own age who took care of the poor.’’

Questions have been raised about Mother Teresa’s legacy, as well as criticism of the Vatican’s decision to make her a saint so quickly.

Asked about the controversy, O’Malley laughed. “When they beatified her in 2003, I said they should just canonize her there and then,’’ he said. “This is redundant.’’

Maria Cramer can be reached at mcramer@globe.com. Follow her on Twitter @globemcramer.