With a small crowd welcomed back in for the decider, after Auckland’s lockdown forced the third and fourth games behind closed doors, the hosts enjoyed the ideal finale to the series after Australia had fought back from 2-0 down to level.
Guptill was named Player of the Match after smashing 71 from 46 balls, including four sixes and seven fours, as they coasted home with 27 balls left.
But New Zealand did the damage with a disciplined display with the ball, restricting Australia to 8-142 from their 20 overs after winning the toss.
New Zealand skipper Kane Williamson said: “Incredibly hard fought series, momentum shifts throughout.
“To adjust on this surface after the first two games on this pitch was very pleasing. We know how strong the Australian side is, we just wanted to put on a much improved performance.
“In some ways we got exposed on that surface. It was a little better today and a really good all-round performance.”
Ish Sodhi, who was named Player of the Series, took 3-24 while Tim Southee and Trent Boult both took two wickets and bowled economically.
Matthew Wade top scored for Australia with 44 from 29 balls in a 66-run partnership with captain Aaron Finch but the visitors slumped with only 2-74 from the final 10.
Guptill eased any nerves chasing a below-par target with his aggression alongside Devon Conway (36 from 28), combining for a 106-run opening partnership.
Glenn Phillips came in and finished the job with 34 not out from 16, after Riley Meredith took two wickets in two balls.
Finch said: “We probably just weren’t aggressive enough with the bat. We kept losing wickets at regular intervals. Couple of us put time in the innings and didn’t go on.”