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 around 12 metres long, 12 tonnes in weight and 10 years old.
Around 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 research projects had been tracking the species around the gulf since the mid-1990s.
"What we know now is they use different foraging strategies when they are feeding on different prey items, and this is unusual for baleen whales," she said.
"So there is a study going on looking at the energetics and mechanics of that, and the advent of drones has been a really useful addition for scientists throughout the world studying their foraging behaviour.
"AUT using drones to capture this footage of Bryde's whales in the Hauraki Gulf adds to our knowledge of the species throughout the world."