"They were taking on water and couldn't stop the ingress of the water and were going to abandon the yacht," Blakemore said.
"We then lost communications with them just after getting their position - which was about 50 nautical miles of Niue island."
The pair jumped into a liferaft and RCCNZ immediately put out a call to other vessels in the area to ask if they could assist.
Two yachts, Inspire from New Zealand and Filizi from Greece, were located around 10 miles away and quickly responded.
Blakemore said by the time the Danish pair were rescued around 8.45pm, their damaged vessel was taking on water very quickly.
"When the survivors were picked up out of their liferaft, the Inspire advised the Gwendoline was sinking rapidly," he said.
"The Gwendoline is a Danish vessel and had a male and a female onboard, both from Denmark. They were both rescued, by the Filizi and Inspire, and are now safe and well so overall, a successful rescue."
The rescued pair are currently onboard the Filizi, Blakemore said, with it and the Inspire heading towards Tonga. They will arrive around midday tomorrow.
RCCNZ was unaware what object Gwendoline had struck causing it to sink, and wasn't sure if the vessel itself had also sunk.
In case it is lying in the water just below the surface, a warning has been put out to boaties in the area to keep an eye out, Blakemore said.
Meanwhile, RCCNZ search and rescue officer Mike Roberts stressed the importance of having communications equipment onboard vessels.
"This shows the critical importance of working communications equipment and the absolute necessity to carry survival equipment, especially when sailing offshore," he said.
Roberts said the Greek and New Zealand yachts that answered the call for help did a "marvellous job" getting to the site.
"The abandoned yacht was described by those who assisted with the rescue as being seen to be sinking quickly."
