Needing 19 runs off Mitchell Starc's final over, New Zealand milked 13 runs off the first four legitimate deliveries to keep the heat on Australia.
"That was awesome," Australia captain Pat Cummins said after their fourth win in six matches.
Glenn Phillips broke the burgeoning stand by taking a return catch to dismiss Warner, but Head raced to a 59-ball century.
New Zealand were uncharacteristically sloppy in the field, dropping five catches, with Head the beneficiary on two occasions.
That left Ferguson with the job of hitting the final delivery for six, but he drilled it straight to the cover fielder instead.
Persons:
Arun Jaitley, Labuschagne, David Warner, Adnan Abidi, Travis Head's, Ravindra, Daryl Mitchell, James Neesham, Mitchell, Neesham, Lockie Ferguson, Pat Cummins, Australia's, Glenn Phillips, Warner, Phillips, Glenn Maxwell, Josh Inglis, Pat Cummins clobbered, Devon Conway, Will Young, Josh Hazlewood, Mitchell steadied, Maxwell, Cummins, Ferguson, Tom Latham, Amlan Chakraborty, Hugh Lawson
Organizations:
Cricket, ICC Cricket, New Zealand, Himachal Pradesh Cricket Association, New, Mitchell Starc's, New Zealand milked, Kiwis, Warner, Zealand, Thomson
Locations:
Australia, Netherlands, New Delhi, India, Himachal, New, New Zealand, Starc