“It’s been a fun ride, like I said yesterday (Saturday). I’ve loved every bit of it,” Finch, who will continue to lead Australia in Twenty20 games, said.
“Sitting around having a beer with your mates in the change room after you win a game or a series is the thing that I miss the most but we’ll definitely enjoy tonight.”
Put into bat, Australia slumped to 16-2 in the sixth over after losing both openers.
Having secured the Chappell–Hadlee Trophy with a match to spare, Australia rested David Warner for the dead rubber.
Josh Inglis could not make the most of the opportunity and scored 10 before Trent Boult had him caught behind.
Finch made five in his 146th ODI before being bowled by Tim Southee, finished his ODI career with 5,406 runs including 17 hundreds at an average of 38.89.
Smith added 118 runs with Marnus Labuschagne (52) to steady the innings and 63 more in quick time with Alex Carey to drag Australia back into the contest.
Smith hit 11 fours and a six before falling to Mitchell Santner in the 45th over trying to accelerate after taking Australia past the 200-mark.
Carey’s unbeaten 42 was strewn with unorthodox shots and Cameron Green clobbered two sixes in his 25 not out.
New Zealand got off to a strong start in their chase but Smith took a low catch to send back Devon Conway (21) and break the opening stand.
Finn Allen made a breezy 35 but New Zealand slumped to 112-5 after skipper Kane Williamson (27) was run out in the 28th over.
Cameos by Jimmy Neesham (36), Glenn Phillips (47) and Mitchell Santner (30) dragged them back into the game before Mitchell Starc claimed the last two New Zealand wickets in successive deliveries to seal victory for the hosts.