The family, which included a young boy and girl, made an emergency radio call from Beveridge Reef – a remote reef 250 miles south east of the small island of Niue, the Rescue Coordination Centre of New Zealand (RCCNZ) said.
Search and rescue officials said it was “very fortunate” that a nearby vessel – the sole craft in the vicinity – was monitoring the emergency channel and able to assist.
The captain of the Dona Catharina, the ketch that rescued the family, said they were now resting and recovering after the overnight ordeal. He did not disclose the identity of the family.
Speaking from a satellite phone aboard the ship, captain Martin Vogel said: “They were pretty distressed but they’re all sleeping now.
“Honestly, they’re coping remarkably well.”
The 50ft catamaran, Avanti, was taking on water but was “well aground”, enabling rescue crews to wait until daylight before collecting the family by lift raft at around 6.30am.
The family left the vessel, which is now likely to break up on the reef, with their passports, some clothes and “a few treasured items”, captain Vogel added.
He said the family included a boy and a girl aged about 13 and 11.
RCCNZ Senior Search and Rescue Officer Geoff Lunt said: “The skipper of a 18 metre steel ketch Dona Catharina answered the emergency radio call from our Maritime Operations Centre within seven minutes.
“It was very fortunate they were anchored in the lagoon and listening to the distress channel at 2.30am.”
He said the boat, manned by seven crew members, was taking shelter as it sailed from New Zealand to Niue to help with a study of humpback whales.
Beveridge Reef is normally submerged with a small part visible at low tide.
Always a danger to shipping, it has been blamed for a number of vessels running around, including a fishing boat, the fibre-glass Nicky Lou, which is visible on the reef.
The lagoon inside the reef can provide calm water for boats but the Avanti had run aground on the opposite side from the lagoon’s narrow entrance.