With Finch’s impetus, Australia made 156-6 batting first before New Zealand foundered on a slow pitch, bowled out for 106 in 18.5 overs.
Tim Southee has been reprimanded for breaching Level 1 of the ICC Code of Conduct during the third T20I against Australia.
After a string of low scores, Maxwell entered demolition mode in the third T20I and launched two mammoth sixes in the 17th over.
Martin Guptill returned to form with a sensational knock before Marcus Stoinis and Daniel Sams almost got Australia over the line.
Martin Guptill whacked eight sixes and six fours during his sensational knock to leapfrog Rohit Sharma's record of most sixes in T20Is.
The left-handed batsman's previous four T20 scores were - 93*, 91*, 69, 50 in the Super Smash.
New Zealand struggled early against Australia pacemen Daniel Sams, Jhye Richardson and Kane Richardson before Conway led a concerted rival.
Suzie Bates has been ruled out of the remaining two ODIs against Australia after sustaining a shoulder injury in the first match.
Needing eight off the final over for victory, Kerr belted Megan Schutt for consecutive boundaries to steer New Zealand to 125-5 and victory with three balls to spare.
Luke Ronchi was 24 not out off 17 balls, including three fours and a six, with Blackcaps captain Kane Williamson unbeaten on 16.