Olga Tanon and Rivera's children were among those performing at the Gibson Amphitheatre in Universal City, where thousands of fans gathered to salute the "Diva de la Banda."
Among the guests were famed Mexican singers Marco Antonio Solis, Ana Gabriel and Joan Sebastian.
A red casket sat onstage amid a sea of white roses, as images of Rivera played on a big screen.
While most of the speeches and songs were delivered in Spanish, Rivera's children spoke in English, often directly to their late mother.
"We're not here to mourn the death," said son Michael, 21. "We're here to celebrate the life and graduation of a singer, an entertainer, a diva, a fighter, an entrepreneur, a philanthropist, and more than anything, a mother—the best mother."
He then called for 27 seconds of silence for the victims of the massacre in Newtown, Conn.
Rivera's youngest child, 11-year-old Johnny, was heartbreakingly poised as he said, "The person that everyone's talking about is my mom."
"Mama, I've been crying so much these last few days. I miss you so much," said the little boy, wearing a red bow tie like many of his family members. "I hope you're taking care of my dad and I hope he's taking care of you, too.
Rivera's brothers and sisters spoke lovingly of the singer, calling her "the queen of queens" and an "eternal diva." Her father said Rivera's "happiness, smile and care for the public will never be forgotten." He then performed a song he wrote about his daughter, a woman who rose from humble roots to become "la Diva de la Banda."
One of Rivera's brothers said his sister "made it OK for women to be who they are. Jenni also made it OK to be from nothing with the hopes of being something."
The family asked that Latin radio stations play Rivera's song "La Gran Senora" at noon Thursday in her honor.
Hundreds of Rivera's fans converged outside the venue, hoping to gain access to the service. Others bought advance tickets for $1.
The service was closed to most media, although a broadcast of the proceedings was made available.
The burial will be private.
Rivera and six other people died Dec. 9 in a northern Mexico plane crash that remained under investigation. Rivera, a mother of five children and grandmother of two, was 43.
Rivera sold more than 15 million copies of her 12 major-label albums. Her soulful singing style and honesty about her tumultuous personal life won her fans on both sides of the U.S.-Mexico border. She was also an actress and reality TV star.
Born in Los Angeles, Rivera launched her career by selling cassette tapes at flea markets. By the end of the 90s, she won a major-label contract and built a loyal following.
Many of her songs deal with themes of dignity in the face of heartbreak, which Rivera spoke of openly with her fans.
She had recently filed for divorce from her third husband, was once detained at a Mexico City airport with tens of thousands of dollars in cash, and publicly apologized after her brother assaulted a drunken fan who verbally attacked her in 2011.