It was the first occasion when any Australian side was all out within 25 overs. In reply to New Zealand's 307-8, Australia were all out for 148 in the 25th over.
The run rate slowed with the tailenders but a total in excess of 300 at Eden Park, even with its short boundaries, was competitive.
Australia were never seriously in contention with their reply. Their innings began to unravel at the very start as Henry and Boult ripped out the top order to have the tourists reeling on 41-6 after nine overs.
"Our bowling effort was one of the best we have put out for a while," captain McCullum said, while Australian skipper Steve Smith felt 300 was a gettable target until Bould and Henry fired up.
"Losing six wickets in the first 10 overs you're not going to win too many games when you do that," he said.
Henry, a surprise omission from the New Zealand team for next month's World Twenty20 championships, continued the form that made him New Zealand's leading bowler in their recent series wins over Sri Lanka and Pakistan. In his first over he had Shaun Marsh caught in the slips for five with a ball that moved across the left-hander. He followed up with the dismissal of Steve Smith, bowled for 18, and George Bailey for two. Boult meanwhile removed David Warner for 12 and claimed Glenn Maxwell and Mitchell Marsh without either scoring.
Warner was dismissed lbw after being hit on the front pad and after discussion with Bailey at the other end he decided to walk.
However, replays showed that had he appealed the dismissal, it would probably have been overturned. Matthew Wade and James Faulkner attempted a rescue mission for Australia with a 79-run stand for the seventh wicket, but when they fell six balls apart the innings was effectively done.
Spinner Mitchell Santner came on for his one over of the game and took the last two wickets of Kane Richardson and John Hastings with his first two deliveries to finish the match sitting on a hat-trick. But the main bowling damage was done by Boult with three for 38 and Henry with three for 41.
Guptill and Nicholls provided the backbone for New Zealand after McCullum, in his final appearance at Eden Park, ignited the innings in typical swashbuckling fashion. After swinging wildly at the first eight balls he faced, McCullum found his target and whacked two sixes and two fours off four consecutive Josh Hazlewood deliveries.
Guptill joined the action, hoisting Kane Richardson on to the roof of the stadium, as New Zealand -- having one run on the board after 14 deliveries -- raced to 27-0 after 19. McCullum left the ground to a standing ovation when his innings ended on 44 off 29 balls with five fours and three sixes.
Kane Williamson fell for a duck but Guptill and Nicholls put on 100 for the third wicket before Guptill was run out. He faced 76 balls and clouted eight fours and five sixes but there was no one following who could maintain the momentum.
With his dismissal, four wickets fell for 53 runs in 12 overs, with Santner's unbeaten 35 at the tail the only other innings of note. The second game in the series is in Wellington on Saturday.
(With inputs from agencies)