The $60,000 machine arrived at the zoo two weeks ago, and this morning's check-up was only the second time it had been used, following a similar check on Anubis' brother Osiris last week.
It was the first time Anubis has had a check-up since 2007, so the team was being thorough, taking extensive x-rays of his body, as well as blood tests, and checking the condition of his teeth and paws.
They were particularly on the look out for signs of arthritis and kidney problems - the two conditions most likely to affect older cheetahs.
The lengthy process drew some attention from visitors, who gathered around the medical room's window to watch the vets at work.
Luckily for the cheetah, nothing major was found, though blood test results won't come through until today, and the team will also spend more time examining the x-rays.
"We still have to look in detail, because we took so many and we did all these different [angles], we're going to really look in detail to see for small changes or small signs of arthritis," Dr An Pas said after the three-hour procedure.
The check-up "went really well", she said, and the machine had "worked really well on this cheetah".
"It helps us a lot with monitoring," Dr Pas said.
It can measure heart rate, temperature, blood pressure, and the amount of oxygen and carbon dioxide in the blood - saving one of the staff from doing it - and then charts all the readings into detailed graphs for the vets to examine afterwards.
Auckland Zoo is the first zoo in New Zealand to have a Tafonius machine, senior vet manager Dr James Chatterton said.
The machine is capable of being used on animals from 15kg to 1500kg, and is mobile, so vets can take it into enclosures if needed.
It monitors an animal's breathing under anaesthetic much more closely than a human can, and ensures the animal is breathing normally - fitting in almost exactly to their natural breathing rhythm, Dr Chatterton said.
Cheetah fact-file
• Scientific name: Acinonyx jubatus
• Conservation status: Vulnerable
• Cheetahs are the fastest animal on four legs, capable of reaching speeds of up to 110km/h for up to 500m.
• They can live for around seven years in the wild, and between 10 to 15 years in captivity.
• Cheetahs are the only big cat that can purr. But they cannot roar like a lion or tiger.
• Auckland Zoo's two cheetahs are called Anubis and Osiris, named after Egyptian deities. They are brothers who were hand-reared by staff at the zoo since they were 10-months-old.