The 38-year-old was with two companions when she fell into a stream inside the Luckie Strike Cave at about 2.35pm, suffering a broken hip and losing three teeth.
Her companion managed to pull her from the water and covered her with a survival blanket before seeking help. Furket was conscious at the time her companion left her.
The incident occurred about 1100 metres into the cave which is 15 kilometres from the Waitomo Township. It appears that Furket unhitched herself from a traverse line on a slippery ledge just prior to the fall.
The cave has been described by a police spokesman as a moderate scramble, which required climbing, crawling, abseiling, and squeezing through wet and dry passages and up waterfalls. Another says there's crawling room only in some parts.
About 25 caving experts, police, search and rescue and St John Ambulance staff worked for up to 10 hours to successfully rescue her from the cave.
She was finally freed at 1.30am on Friday after a "challenging" rescue, which involved her being brought through the narrow and twisting caves suspended on a stretcher.
She was airlifted to Waikato Hospital.
The combined rescue effort has been praised by police. They say the rescue was quite technical due to the high traverse lines and narrow passage ways.
The experienced recreational caver is a member of the Nelson Caving Club.
Luckie Strike, about 20 minutes drive west of the village of Waitomo Caves - has a reputation among cavers as one of the most physically demanding and beautiful caves in the country.
Last year, Motueka doctor Michael Brewer found himself in a similar situation - injured and trapped 400 metres underground in the Middle Earth cave under Takaka Hill near Nelson.
It took nearly three days and a highly complicated rescue effort involving about 50 cavers to extract him.