The outcome of the match is academic, as New Zealand have an unbeatable 2-0 lead in the series, but Australia are desperately seeking to extract one positive outcome from the tour.
Hayden let rip on the attack, hitting the highest one-day score by an Australian, eclipsing the previous best of 173 by Mark Waugh.
Hayden cashed in on New Zealand's decision on Tuesday to lay off their two most experienced bowlers, Shane Bond and Daniel Vettori.
His 181 came from 166 balls and included 10 sixes -- an Australian record and one short of the world record of 11 jointly held by Pakistani Shahid Afridi and Sri Lanka's Sanath Jayasuriya.
Hayden tempered his stroke play early and his 50 came up in 82 balls, but as his confidence grew so did his powerful drives.
When a foot injury in the latter half of the innings forced him to call for a runner, Hayden stepped up the boundaries to reduce the amount of movement.
Without Bond, New Zealand's new-ball attack of James Franklin and Daryl Tuffey lacked genuine firepower forcing the innovative Stephen Fleming to delay his final powerplay to the 36th over.
In that five-over spell, Australia scored 37 for the loss of Brad Haddin's wicket before stepping up the pace to add another 125 in the final 10 overs.
Shane Watson, pushing for the role of opener at next month's World Cup, was the perfect partner for Hayden at the head of the innings, chiming in with 68 before falling leg before wicket to Jeetan Patel.
But none of the other Australian batsmen were in long enough to post scores of note.
Haddin made 38 from 65 balls, while Mike Hussey and Cameron White both made 13 and Brad Hogg 12.
Adam Voges, in his first one-day international, was not out five.