Australia won by six wickets, but Waugh made his second duck in a row to continue a poor sequence with the bat since replacing Mark Taylor, who remains Test captain for the forthcoming series against South Africa.
Chris Cairns made New Zealand's 141-run total look defendable when he picked up three wickets in 10 deliveries, including the Waugh twins, Steve and Mark, in three balls, both caught behind by Adam Parore.
New Zealand had fought back stoically from 75 for seven and failed by only three balls to bat out their regulation 50 overs.
At one stage they lost three wickets in three balls, starting when Shane Warne had Craig McMillan caught at first slip with the last ball of his first over.
The second wicket came in unusual style when Roger Twose was run out without facing a ball from a deflected drive, backing up at the bowler's end. Nathan Astle snicked Adam Dale's next ball with a rash shot.
Chris Harris, batting with considerably more application and resolve than some of his higher-order team-mates, hit 62 not out. Paul Wilson took three wickets for Australia on his one-day debut.
Rick Ponting scored 60 off 92 balls to steer the Australians home and into second place on the triangular series behind the leaders South Africa.
Ponting and Michael Bevan, with 42, put on a match-winning 95-run partnership for the fourth wicket. Australia secured victory with more than 11 overs remaining.
Matthew Elliott, Australia's opening batsman, suffered a knee problem during training with Victoria and is doubtful for the first Test against South Africa at Melbourne on Boxing Day.