"He was a shining star of the greatest generation," fellow Hawaii Democratic Sen. Daniel Akaka said at the service.
Akaka, who served with Inouye for 36 years, also highlighted Inouye's role in steering federal money to build roads, schools, housing and other infrastructure in Hawaii over the decades, from the beginning of statehood.
"Dan Inouye is Hawaii, and Hawaii is Dan Inouye," Akaka said.
Inouye's chief of staff, Jennifer Sabas, said Inouye was calm, in control and giving out instructions until the very end. Then, "he penned 'aloha,' and went on to a better place," she said.
"Aloha, boss," she said in closing, as she stood beside his flag-draped coffin.
Several services have already been held in Washington and in Hawaii for Inouye. He lay in state at both the U.S. Capitol Rotunda on Thursday and the Hawaii state Capitol on Saturday. A public service is planned for Friday on Kauai. His burial is expected to be a private, family event.
Obama eulogized Inouye during a service at Washington's National Cathedral on Friday, saying that Inouye's presence during the Watergate hearings helped show him what could be possible in his own life.
The president arrived early Saturday in Honolulu for his annual Christmas family vacation. He made a brief visit to the grave of his grandfather, World War II veteran Stanley Dunham, after Sunday's service.
Associated Press writers Matthew Daly and Anita Hofschneider contributed to this report.
Contact Becky Bohrer at https://twitter.com/beckybohrerap