The Otago arrived alongside Django II at about 5.30pm, with the Laura Bulker on scene shortly after and standing by while the naval vessel carried out the rescue.
The Django's II crew abandoned ship into a liferaft, but as it was being hauled across to the Otago they feared the larger vessel was about to roll over and crush them in the heavy seas, and they cut the rope.
The Otago then sent a swimmer into the water with another rope, to tie the liferaft on again and bring it alongside.
The crew are now safely on board the Otago, which is en route to Devonport in Auckland and expected to arrive around 9am tomorrow.
RCCNZ Search and Rescue Mission Coordinator Neville Blakemore praised the Otago and Laura Bulker for their prompt response to the request for help, and the skilful rescue in difficult conditions.
The yacht and liferaft were still afloat when the vessels departed the area, and a navigation warning has been issued to advise mariners of its position.