The Australia skipper smashed 164, the highest ODI score at the Sydney Cricket Ground, to lead Australia to 324 for eight.
In response, New Zealand could only muster 256 all out in 44.2 overs.
The innings, the seventh highest by an Australian, surpassed South Africa's AB de Villers 162 at the same ground in last year's World Cup.
Intriguingly, the series also doubles as an audition for Australia's upcoming Test series against Pakistan with middle-order batsman Travis Head, all-rounder Mitchell Marsh and legspinner Adam Zampa on the fringe of Test selection.
The dismissal of BJ Watling was special for the Australians as their skipper Smith made a full fledged dive to his left and picked a stunner at backward point and Head described it as a "game changer".
In response, New Zealand did have a batsman leading from the front, just like Smith, with Martin Guptill scoring a ballistic 102-ball 114.
However, Guptill was caught at the second attempt by substitute Glenn Maxwell at mid-wicket at the end of the 33rd over with 140 still needed - and Australia went on to end a run of five successive one-day defeats.
Jimmy Neesham put on 92 for the third wicket with Guptill before he holed out to Hazlewood off Mitchell Starc.
Smith's top-ranked team suffered a 5-0 ODI series drubbing in South Africa in October and looked shaky again when reduced to 92 for four in the 21st over.
But Smith, who could have been out three times, led a swashbuckling recovery and thwarted opposition bowlers to put his side in the ascendancy. Like I said before, we've got to take every opportunity, especially when you're playing against Australia in Australia.
"It's nice to get my highest score at my home ground and post a huge total".
New Zealand also arrive with no Ross Taylor, who is recovering from eye surgery.
Glenn Maxwell has declared he's dimmed the lights on The Big Show and promised a more measured mindset in his return to Australia's one-day side. For New Zealand, Jimmy Neesham showed glimpses of being a good all-rounder in the future with more and more exposure to global cricket.
Smith joined David Warner and the pair put the early setback behind them before a dream moment for Lockie Ferguson ended the stand, Warner chopping on to give him a wicket in his first over in worldwide cricket.
Smith reiterated the point he made before the game that the saga had not affected his chances of selection, adding they simply chose to go with Head. Kane Williamson's men will be eager to retain the Chappell-Hadlee trophy, which they won by beating the Australians at home earlier this year. In the first over of the match, Aaron Finch played on to Henry for a golden duck, and David Warner also chopped on within the first ten overs of the game, handing debutant Lockie Ferguson a maiden global wicket in his first over.