The aircraft was guided by a chain of burning fuel barrels, makeshift beacons in Antarctica's 24-hour darkness, and the pallets had to be picked up within minutes of hitting the ground.
The US Air Force crew had to find the parachute drop point in the dark and shove the pallets out a side door before dwindling fuel forced them to head back to Christchurch in New Zealand.
The mission had been organised to help a 47-year-old woman on the US scientific team based at the South Pole, who had discovered a lump in her breast.
In the middle of Antarctica's nine-month winter, with temperatures consistently below minus 60C, no daylight, and only a tiny air strip at the research station, there was no possibility of airlifting her out for hospital tests until in October at the earliest. The Antarctic winter lasts from February to late October, when there follows a brief, three-month summer.
The only option, therefore, was to drop equipment and medicine from the air in the hope that any necessary treatment could be carried out at the base.
That, however, was an elaborate logistical exercise fraught with peril, necessitating a 6,000 mile non-stop round trip to the South Pole and back, mid-flight refuelling, low flying to accomplish the air drop, and the risk that the aircraft hatch could freeze open or shut as the packages were dropped.
Even then, there was no guarantee that the equipment would not be damaged by the impact or would not be retrieved in time to escape harm from the extreme cold.
"There are 40-to-60mph winds there," said Captain Bill Barksdale, an Air Force spokesman at the Tacoma air force base near Seattle, Washington.
"It's 60 to 80 degrees below zero and there is perpetual darkness. All of those factors make this mission dangerous. But we've made this flight before in the summer and our crew is familiar with what needs to be done. It's just that we haven't made a midwinter drop in several years."
The Air Force C-141 Starlifter transporter, with a crew of 19, was dispatched from Tacoma air base laden with equipment and drugs. It included two 380lb ultrasound scanners and video-conferencing equipment to enable the one doctor at the research station's rudimentary clinic to consult specialists in the US. Everything was sent in duplicate, in case there was damaged to one.
The aircraft stopped over in Hawaii before proceeding to Christchurch in New Zealand. It then set off on its 14-hour non-stop flight to the South Pole and back. It is thought to be the longest peace-time mission ever flown by the US Air Force. However, the weather at the Pole - light snow, and a ground temperature of minus 65C - was said to be good.
The runners of the aircraft's side door were specially lubricated to prevent freezing, and the crew were equipped with oxygen masks and protective clothing.
The six pallets were dropped by parachute during two low-flying passes over the Amundsen-Scott South Pole station, which lasted around 20 minutes. The pallets were dropped about 50 yards from the base.
With the risk that the pallets would freeze to the ice, ground staff from the base had an estimated seven minutes to rush out into the darkness and retrieve them.
An official of the National Science Foundation project, which is based in New Zealand, confirmed that the mission had been successful.
"Six pallets are on the ground, and all six have been retrieved successfully by base staff within minutes of them hitting the surface," the commander of the Antarctic support group, Colonel Richard Saburro, said.
The woman beneficiary of the operation has not been named, but she is one of 41 members of a team called Antarctic Support Associates, a company that provides services for the US National Science Foundation station.
The station is about as isolated a spot as you could find on the planet; the laboratories and living quarters are about 840 miles from the nearest populated site, which is another research station on the Antarctic coast.
Also included in the packages was fresh food and post for the scientists - an unseasonal surprise for the scientists who expect to be completely cut off from the world during the Antarctic winter.
The aircraft pilot, Major Greg Pike, said that blowing snow kept the crew from seeing the blazing barrels until about two miles from the drop zone as they approached the area at about 200mph.
"Conditions down there visibility-wise to pick up the runway were a lot different from what we were expecting," he said. "We had to make our movements to get on alignment right at the end to get on to the drop zone.
"I would definitely describe this as my most difficult mission I've ever flown of any air drop I've ever done," Major Pike said. "After all, the whole thing is a loss if we don't put it where they can get it."
The crew reached Christchurch at about midnight last night. A tanker aircraft from Travis Air Force Base in California went along on the mission to refuel the Starlifter in flight.
In New Zealand, Colonel Saburro said the crew at the polar station had been overjoyed by the extraordinary mission which had been undertaken at such a risk on behalf of one of their colleagues. "They welcome even the sound of an airplane above - it gets them excited and connects them back to the rest of the world," he said.
"We have a message from the South Pole that they are delighted and thanking everyone for their assistance.
"They are very happy. The worst is over. We are all very relieved at this point."