Guptill plundered nine sixes and six fours to score 105 off 54 balls as New Zealand finished on 243 for six after winning the toss and electing to bat at Eden Park.
It took Guptill's international T20 career total to 2,188 runs, surpassing compatriot Brendon McCullum's 2,140, with India's Virat Kohli the next highest on the all-time list with 1,956.
Guptill's 49-ball century was New Zealand's fastest T20 ton and the team total of 243 equalled the highest ever posted by the Black Caps.
In all, New Zealand's innings included 18 sixes and 14 fours.
Australia are unbeaten so far in the series and will need to be at their best to overhaul the mammoth target and maintain their record.
Australia have already reached the series final and a New Zealand win would also guarantee them a spot in the decider at England's expense.