The couple and their two children had been sailing through the remote Beveridge Reef, 400km (250 miles) southeast of the island of Niue, when their 15m catamaran ran aground.
An emergency radio call was put out at 2.30am local time and was picked up by the ketch sailboat Dona Catharina, which happened to be carrying out whale research nearby.
The ship’s skipper answered the call within seven minutes.
According to the Rescue coordination centre of New Zealand, When they reached the catamaran, it was taking on water but was well aground on the reef.
After waiting a few hours until daylight, the rescue crew were able to take a dinghy to collect the family.
There had been no other vessels in the vicinity.
Senior search and rescue officer Geoff Lunt said the catamaran is likely to break up on the reef.
He added that the family are currently “comfortable onboard the ketch, within the safety of the lagoon”.
“We would like to thank the crew of the ketch and all the rescue services involved in tracking vessel locations and successfully rescuing this family,” he said.
The group is to sail to Niue in the next few days.