Fit-again all-rounder Shane Watson marked his return from three games out with a calf injury by scoring a blistering 65 not out.
Hayden's 103 off 100 balls, with two sixes and 10 fours, saw the tournament's leading run scorer equal the record for most hundreds at a single World Cup held by Australia's Mark Waugh (1996) and India's Sourav Ganguly (2003).
It was also the 35-year-old Queensland left-handed opener's fifth hundred in 21 one-day international innings after he was dropped for the Champions Trophy in India in October and November, a run that included his Australia record 181 not out against New Zealand in Hamilton in February.
But New Zealand were without ill fast bowler Shane Bond and injured pace bowling all-rounder Jacob Oram.
Impressive off-spinner Jeetan Patel took two for 48 in a match which was the last group game for two teams who had already made sure of their semi-final places.
Watson countered with a 32-ball knock featuring four sixes and four fours. He ended the innings by slashing left-arm quick James Franklin over cover for six.
Franklin took three wickets but his eight overs cost an expensive 74 runs.
Mark Gillespie, Bond's replacement, saw his six wicketless overs go for 67.
Together with Australia captain Ricky Ponting (66), Hayden put on 137 for the second wicket after the early loss of Adam Gilchrist.
Franklin, often reliant on swing, took a wicket first ball when Gilchrist, on one, cut a wide delivery straight to Gillespie at third man.
With Australia 28 for one off four overs, New Zealand captain Stephen Fleming gave an unusually early introduction to Patel.
Hayden and Ponting both completed 53 ball-fifties before their 22-over stand ended when the captain chipped a drive off Patel to Ross Taylor at short mid-wicket.
Hayden, against Daniel Vettori in his 200th one-day international, drove the left-arm spinner for three successive fours.
And he went to 96 with a huge straight six off Scott Styris.
But going for another big hit off the medium-pacer he miscued a drive high in the air and Styris, running back, held a superb caught and bowled chance as the ball dropped over his shoulder.
Australia were now 216 for three in the 33rd over.
But when Patel had the hard-hitting Andrew Symonds caught at long-off for 11 by Michael Mason, Australia were 257 for five in the 41st.
New Zealand have won their last three one-dayers against Australia following a clean sweep in February's Chappell-Hadlee series where they also scored two of the three biggest totals to win batting second in one-day international history.
Victory in this match would see New Zealand draw level with standings leaders Australia on 12 points.
But they would need to win by a huge margin to go ahead on run-rate and upset the likely semi-final pairings which currently see them playing Sri Lanka in Jamaica on Tuesday and Australia up against South Africa on Wednesday in St Lucia.
The World Cup final is scheduled for Saturday, April 28 in Barbados.
Australia 348 for 6 in 50 overs (Hayden 103, Watson 65 n o, Ponting 66, Clarke 49, Hussey 37; Jeetan Patel 2 for 48, Franklin 3 for 74) Vs New Zealand (yet to bat).