Michalis Liapis, the Greek culture minister, called the operation - the first of many in the coming weeks - a "historic event of global significance."
Over the next few months, 4,500 antiquities, mostly marble sculptures dating to the sixth and fifth centuries BC, will be shifted into the new Acropolis Museum 400 metres (yards) away from the temple.
On Sunday, crews in three cranes moved a 2.3-tonne section of the Parthenon frieze: a 160-metre-long strip sculpted in relief with some 360 human and 250 animal figures from a religious procession.
Liapis called the transfer "both awe-inspiring and deeply moving."
"For the first time after 25 centuries, the sculptures are being transferred to the new Acropolis Museum," he said
Costas Zambas, the supervising engineer of the project, said the move went off without a hitch, and faster than expected. He said crews had decided not to carry out any transfers if winds are higher than 39 kph (24 mph) - and Sunday was a windy day.
"But everything went off like a dream, totally safely," he said.
The antiquities, insured for €400 million ($567 million), will be wrapped in padded harnesses and packed into styrofoam-filled boxes made of plywood and metal.
The Parthenon sculptures eventually will be exhibited on the top floor of the three-level museum with a view of the ancient temple. The works will be mounted in their original alignment on a model of the Parthenon's upper section.
Designed by architect Bernard Tschumi, the €129 million ($182 million) glass-and-concrete museum is expected to open in late 2008.
"The museum, which is empty in a sense, is now being populated - populated by those sculptures," said Tschumi, who attended the inaugural transfer.
Greek officials hope the new museum will boost the country's long-running campaign to wrest back the British Museum's collection of sculptures from the Parthenon.
"For the first time after 25 centuries, the sculptures are being transferred to the new Acropolis Museum"
Michalis Liapis, Greek culture minister
The works were removed from the fifth century BC temple some 200 years ago - when Greece was still an unwilling member of the Ottoman Empire - by Scottish diplomat Lord Elgin and bought by the London museum, which has refused Greek demands for their repatriation.
Liapis said completion of the Acropolis Museum would repudiate British Museum officials' contention that Greece lacks a fitting venue to display all the Parthenon sculptures together.
But not everybody was happy on Sunday. As the light blue crate with its precious load dangled overhead, dozens of people gathered to protest the scheduled demolition of an Art Deco architectural gem and its late 19th-century neighbour that block the view of the Acropolis from the new museum.
A banner on the new museum's railings read: “Don't knock them down; we don't have enough of them.”
The Parthenon was built between 447-432 BC, at the height of ancient Athens's glory, in honour of Athena, the city's patron goddess.
It survived virtually intact - until a massive explosion caused by a Venetian cannon shot in 1687, when the Parthenon was in use as a gunpowder store by the Acropolis's Turkish garrison.