The team was using a custom-built multi-rotor UAV, one of a number of drones used by AUT's Institute for Applied Ecology in their conservation and ecology research.
It flew at a distance of at least 40 metres from the whales, while recording clear, detailed footage.
The adult whale was estimated to be about 12 metres long, 12 tonnes in weight and 10 years old. About 50 Bryde's whales are estimated to live year-round within the Hauraki Gulf, mixing with another 150 seasonal visitors; one of the few resident populations of this species in the world.
Dr Rochelle Constantine, a senior lecturer at the University of Auckland's School of Biological Sciences, said long-term projects had been tracking the species around the gulf since the mid-1990s.