"Cardinal Bevilacqua was an extraordinary man of the church," Chaput said.
"He loved his people, he loved Philadelphia and he carried the burden of leadership at a very painful time for Catholics in this country."
Bevilacqua was archbishop in 2002, when several members of the Philadelphia clergy were accused of sexual abuse.
"He gave everything he had to his ministry as priest and bishop," Chaput said.
Monsignor Louis D'Addezio provided the Mass' homily, paying tribute to one of his closest colleagues.
"I share with you today my personal memories that I have of my bishop, my fellow priest and my dear friend," said a teary D'Addezio. "These are the sides of Cardinal Bevilacqua that the public seldom saw."
D'Addezio remembered the lighter side of life with Bevilacqua, including how he liked his pasta (without cheese) and his annoyance with long ceremonies.
He also shared memories of Bevilacqua's yearly Thanksgiving ritual of visiting hospital patients and his habit of spending time with sick priests, a practice he continued long into his retirement.
Above all, D'Addezio said, Bevilacqua was a man who cherished his family.
"The love his Eminence had for each of you had no limit," he said to the members of the Bevilacqua family in attendance, including the late cardinal's brother, sister, nieces and nephews.
"You brought nothing but joy to his life."
Brother Joseph Willard, F.S.C., who served as Bevilacqua's associate vicar for administration, also was at the service, which he called a "fine tribute to a man of generosity and sincerity."
"He was a man that loved the people, loved to be with the people, loved to serve the people and loved to be in their presence," Willard said of Bevilacqua. "There were times when he would stay for hours after an event, just to shake hands and make time for people who wanted to see him."
Following the Mass, Bevilacqua was interred in the cathedral's crypt alongside other former leaders of the Archdiocese, including Archbishops James Wood and Patrick Ryan and Cardinals Dennis Dougherty and John Krol.