Ms Neale and her partner, Daryl Hewer, had been attempting to sail from Dunedin to Jackson Bay on Wednesday but abandoned their boat in rough weather off Fiordland.
The Rescue Co-ordination Centre New Zealand dispatched a rescue helicopter from Te Anau and, using night-vision equipment, the crew located the couple about 11.35pm.
Ms Neale was spotted on the rocks, while Mr Hewer was seen on the beach, near the grounded boat.
"It was just impossible. Being night-time, [there was] bad vision and a lot of wind," he said.
It was decided he would be winched ashore to assist the pair.
The helicopter crew then retrieved sleeping bags from nearby Kisbee Lodge and dropped one to Ms Neale on the rocks, and another to Mr Hewer.
With the helicopter to return at dawn, Mr Burnby spent the night with Mr Hewer on the beach, "extremely worried" about the safety of Ms Neale.
She had wedged herself on to a "wee ledge" on the far side of a rock and the pair could not see what was happening to her.
"I did not think she was going to live through it. I thought she would get washed off the rocks," Mr Burnby said.
He got Mr Hewer "comfortable", wrapped in sleeping bags and out of the weather, and tried to let him sleep.
"Then it was a case of sitting and waiting until first light this morning."
It was hard for Mr Burnby to do nothing, but he knew they "had done our best" and it was "just not safe for us to go in".
They were finally retrieved at 5am yesterday and flown to Kisbee Lodge at Preservation Inlet, where Mr Burnby tended to Ms Neale's minor injuries before they carried on to Te Anau.
"It had a very good ending - better than I was expecting," he said.
Sergeant Tod Hollebon, of Te Anau, praised the search and rescue effort, saying the group used "a lot of initiative in very trying conditions".
He said salvaging of the boat, which he understood did not belong to the couple, was usually the responsibility of owners and their insurance companies.
RCCNZ search and rescue mission co-ordinator Ramon Davis said the incident was a "clear case of the importance of carrying good communication equipment", as well as the right navigation equipment and knowing how to use it.
"If these people had not been carrying an emergency locator beacon, we would not have known where to look for them, as they were well away [from] where the original reports put them.
"They did exactly what we advise all boaties to do, which was to carry two forms of reliable communications equipment, and in this situation it may have saved their lives," he said.
The Haast couple had radioed for help at 7.15pm, saying their vessel, a 9m former fishing boat, had broken down and they were drifting towards rocks near the entrance to Milford Sound.
At 9.38pm, the centre received an emergency locator beacon signal from Puysegur Point, about 185km from where the boat was initially reported to be.
