The home side racked up 307 for eight in their 50 overs in Auckland, and then reduced Australia to 41 for six.
Matthew Wade and James Faulkner briefly threatened an unlikely comeback, but the revival stalled and they were all out for 148 after just 24.2 overs to go one down in the three-match Chappell-Hadlee series.
Boult and Henry whipped out the Australia top six in just nine overs at the start of the tourists’ reply, each taking three wickets to seize control of the match.
Shaun Marsh made five, George Bailey fell for two and Glenn Maxwell and Mitchell Marsh both went for ducks, with David Warner’s 12 and captain Steven Smith’s 18 the only double-figure offerings from the top six.
Wade and Faulkner made 36 and 37 respectively to spare Australia the humiliation of a heavier defeat, but by that stage there was never any serious prospect of making the match a contest.
Spinner Mitchell Santner wrapped up victory, coming on to take two wickets in two balls at the start of the 25th over as he removed Kane Richardson and John Hastings.
The foundations of New Zealand’s total were laid in the opening 10 overs as Martin Guptill and Brendon McCullum enjoyed themselves.
McCullum hit two sixes and two fours off Josh Hazlewood in the third over, while Guptill struck a mammoth 115-metre maximum which cleared the main stand.
The opening pair led the Black Caps to 79 before McCullum fell in the 11th over for 44 off 29 balls, bowled by Faulkner.
After Kane Williamson departed for an eight-ball duck, Henry Nicholls joined Guptill at the crease and they put on exactly 100, before the latter was run out 10 short of a 10th ODI ton after hitting five sixes and eight fours in his 79-ball stay.
Some late-innings hitting from Santner, who finished on 35 not out, ensured the hosts had a decent total to defend, one to which Australia never came close.
Australia were dealt a further blow after the game when Faulkner was ruled out of the remainder of the series with a hamstring injury.