Shaun Marsh took Australia to the cusp of victory before losing his wicket on 49 and the fighting Kiwis set up a tense finish under the floodlights by also dismissing Peter Nevill to leave the home side seven wickets down.
Peter Siddle hit the winning runs, much to the relief of the crowd, to clinch a 2-0 series win over the gallant Black Caps.
Australia won the first Brisbane Test by 208 runs and the second Perth Test was drawn. The match was redemption for Marsh, who has struggled to hold down a place in the Australian team with inconsistent batting performances over his four years at Test level.
The pink ball developed for day-night Tests triumphed over the bat in a fast-paced Test which attracted a total attendance of 123,736.
The aim of the experiment is to bring the crowds back to the long form of the game.
"The bowlers have dominated this game and it's great for cricket," said Australian skipper Steve Smith.
"It has certainly brought the bowlers into the game, particularly under the lights."
It was the first three-day Test match at the Adelaide Oval in 64 years -- since the West Indies beat Australia by six wickets.
"It was an outstanding game of cricket. Obviously completely contrasting to what we have seen in the series," said Kiwi captain Brendon McCullum.
"In terms of an experiment I thought it went off as good as it could do, and the crowd supported it and it was an outstanding game of cricket."
Shaun Marsh had been dropped during the Ashes series in England in August and only came into the Adelaide Test as a replacement for injured number three Usman Khawaja.
He lost his younger brother Mitch during the final session, caught holing out to spinner Mitchell Santner for 28 with 26 runs still needed for victory. Shaun Marsh lost his own wicket when he dabbled at Trent Boult and was snapped up by Ross Taylor at first slip.
Adam Voges, who had earlier shared a valuable 49-run fourth-wicket stand with Marsh, was out early in the final session -- snapped up at second slip by Tim Southee for 28 off Boult.
After being set 187 to win, the hosts were rocked by the double loss of skipper Steve Smith and his deputy David Warner in the space of seven balls.