Australia have fallen at the final hurdle in their T20 tour of New Zealand, roaring back from 0-2 down in the series only to lose Sunday's decider by seven wickets.
Master blaster Martin Guptill powered the Black Caps past Australia's 8-142, which looked short of a competitive total.
Guptill smashed three sixes off one Adam Zampa over - including one out of the stadium and onto the roof of Wellington's 'caketin' - on his way to a thumping 71.
Conway, elevated to open the batting at Tim Seifert's expense, helped the pair notch a century partnership with his own 36.
Riley Meredith gave Australia hope when he removed Conway and had captain Kane Williamson trapped lbw next ball.
In Meredith's next over, Guptill asserted his authority with a booming straight and low drive that missed the Tasmanian by centimetres.
Guptill holed out off Jhye Richardson's bowling soon after, but the damage was done, New Zealand winning with 27 balls left.
Spinners Ashton Agar and Adam Zampa went wicketless in the decider after their efforts helped Australia back into the series.
Australia would rue their own stuttering innings, after winning the toss and electing to bat.
A promising powerplay made way to a mid-innings squeeze, with Williamson throwing the ball to part-timers Glenn Phillips and Mark Chapman - put in the side for the ailing Kyle Jamieson.
Matthew Wade top scored with 44, ending his miserable run with the bat this tour.
Finch (36), Marcus Stoinis (26) and Mitch Marsh (10) were the only others to reach double figures.
Josh Philippe was elevated to opener but looked uncomfortable before being trapped by Trent Boult lbw, while Maxwell found a fielder with his first attempted slog.
Finch was dropped on 32 but cut Ish Sodhi straight to point two balls later.
Sodhi - a strong contender man of the series - took the wickets of Marcus Stoinis and Ashton Agar from consecutive full tosses in the 18th over.
After losing the series, Australia aren't sticking around in the New Zealand capital - chartering a flight home on Sunday evening.
Australian Associated Press
