The enormously popular adventurer died of a heart attack on Jan. 11 at the age of 88.
"In reality he was a colossus, he was our hero, he brought fame to our country ... but above all we loved Sir Ed for what he represented - a determination to succeed against the odds," Prime Minister Helen Clark told mourners.
As the service began, five Sherpas, including one woman, laid traditional prayer scarves on the coffin for Hillary, who had spent more than 40 years working to aid Nepal's development.
The ice ax used by Hillary on his May 29, 1953, conquest of Mt. Everest with mountain guide Tenzing Norgay also lay atop the flag-draped coffin.
One of the 20th century's greatest adventurers, Hillary later made the first motorized overland trip to the South Pole, led a jet boat expedition from "sea to sky" up India's Ganges River and joined an expedition to the North Pole.
The former beekeeper became a humanitarian, building schools, hospitals, health clinics and other facilities in Nepal to aid the Sherpa people of Nepal's mountain region near Everest.
His son, mountaineer Peter Hillary, who has twice climbed Everest, said his father "was a real people's hero" and that helping the Nepali people "really was the great calling of my father's life."
Ang Rita Sherpa, head of Hillary's Himalayan Trust aid group in Nepal, said he was "an idol and inspiration for everybody" who had transformed the lives of two generations of Sherpas.
There were now 6,500 students in 63 schools, as well as two hospitals, a dozen health clinics, a million trees planted, safe drinking water systems, bridges and miles of new trails - a direct result of Hillary's work, he told the service.
Norbu Tenzing Norgay, the eldest son of Hillary's climbing partner, said Hillary's "loved Sherpa people" had "spiraled into mourning only comparable to the loss of a parent" when they heard of his death and had "prayed for his soul and reincarnation."
"Among Sherpas he was revered" as he "had opened Sherpas' eyes to a world of possibilities." His passing meant they should continue and expand his work in the region, Norbu Tenzing added.
In the congregation were dignitaries and diplomats from many nations, including the U.K., U.S., Australia, Canada, India, Ireland, Nepal, Russia and Tonga.
The four surviving members of the original 14-strong 1953 Mt. Everest climbing team attended the funeral service, which ended with the singing of the National Anthem. New Zealand Alpine Club members formed an honor guard outside the church, holding ice axes aloft as the casket was carried through their lines.
At the same time, mountain guides and others gathered at the Sir Edmund Hillary Alpine Center at Mount Cook, New Zealand's highest peak which Hillary first climbed in 1946, to pay respects.
In Antarctica, workers at the New Zealand and U.S. science bases watched the funeral beamed on a special satellite feed.
Students from Sir Edmund Hillary College performed a Maori war dance of farewell near the church before the cortege moved away for a private cremation service. The cortege traveled through the city and past the Hillary family home as thousands of people stood in the streets, some clapping.
Hillary had asked that his ashes be scattered on Auckland's Waitemata Harbor, perhaps to wash ashore "to complete the cycle of my life."
