Captain Kane Williamson had gone for nine and it was soon apparent only Guptill stood between Australia and a 1-0 lead in the three-game series.
BJ Watling fell to a spectacular one-handed diving catch at gully to his left by Australian skipper Steve Smith.
Colin Munro signalled his intentions early with a towering six off Mitchell Marsh, and after becoming becalmed against tidy bowling, made a late flurry.
That included having his bat snap as he slapped a ball towards deep cover.
However three wickets fell for 18 in 29 balls as Australia turned the screw.
Matt Henry hit long and hard but once Guptill departed it was always a long chance.
Earlier, New Zealand's bowlers forgot their lines and were caned by Australia.
There were a pile of painful lessons for New Zealand out of the first innings of the keenly-anticipated opener as Australia got out of a jam at 92 for four to fly to 324 for eight on the back of captain Smith's rollicking 164, the highest ODI score put up at the venerable ground.
But as impressive as Smith's innings was, he had costly letoffs along the way and some witless bowling to help him out.
New Zealand spilled three catches, two off Smith, another off Travis Head, whose stand of 127 for the fifth wicket with his skipper righted the Australian ship and laid the groundwork for a spectacular conclusion.
Smith and wicketkeeper Matt Wade bounced four sixes into the crowd in the space of six balls as New Zealand's bowling fell apart in the closing overs. Their stand was worth a barely believable 83 in only 6.1 overs.
Add in that New Zealand had made a calamitous blunder in failing to refer a denied lbw appeal against Smith on 14 from Trent Boult and it all added up to an awful night in the field.
Smith was struck on his pads by Boult, the pick of the attack, and replays showed it would have hit near the top of off stump.
Excuses could be made that, with only one unsuccessful DRS referral available, New Zealand might have wanted to be careful. The point is Smith is the key Australian wicket and it had to have been worth the punt.
How Smith made them pay. He had been dropped down the leg side one run earlier by wicketkeeper Watling off Boult and on 152 Munro spilled him at square leg.
Throw in Head's letoff, on seven, Henry dropping a regulation catch at deep mid off above his head and it was a sloppy performance.
There were few signs of smart thinking among the bowlers, with precious few yorkers and as skilfully as Smith batted, New Zealand were guilty of handicapping themselves for too much of the innings.
''I had a bit of luck but you try and make the most of it," Smith said. ''The new ball nipped around a little bit but then things got a little bit easier from there."
Too right they did.
Game Two of the series is at Canberra's Manuka Oval on Tuesday.