Smith struck 14 fours and four sixes in his seventh ODI century after winning the toss in the first match of three in the Chappell-Hadlee Series to put his side in a strong position.
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.
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 was could have been out three times, took advantage to lead a swashbuckling recovery as he flailed the Black Caps bowlers and put his side in the ascendancy.
"I had a bit of luck, but you have to take that and make the most it," Smith said after his innings.
"Nice to get a big score on my home ground. I love batting here, it's a great place to play and great to play in front of my family."
Smith was finally out three overs from the end when he skied Trent Boult to Colin Munro at midwicket.
Smith was supported by 52 from newcomer Travis Head, who was dropped by Matt Henry on nine, while wicketkeeper Matt Wade clobbered three sixes off a Jimmy Neesham over on his way to 38 off 22 balls.
Australia made a disastrous start with Aaron Finch playing on to his leg-stump for a duck in Henry's opening over.
Smith gave New Zealand two chances in Boult's third over.
BJ Watling missed a leg-side catch on 13 and one run later Boult's leg before wicket appeal was turned down by the umpire.
New Zealand inexplicably did not call for a review, which showed the Australian captain would have been out.
Smith had a third 'life' on 152 when Munro dropped him at square leg.
David Warner attacked debutant paceman Lockie Ferguson, smashing two boundaries off the youngster's first over before he inside-edged on to his stumps for 24 off 29 balls.
George Bailey was out for 17 off a leg-side catch by Watling off Neesham and all-rounder Mitchell Marsh, batting at number five, was run out at the non-striker's end for one in unfortunate fashion when a Smith drive ricocheted off bowler Neesham's hands into the stumps.
Head put on 127 for the fifth wicket with Smith, before he was caught and bowled low down by Boult.
All-rounder Glenn Maxwell was left out of the Australian line-up after being fined Saturday for his criticism of teammate Wade.
Maxwell was excluded after last week taking a swipe at Wade's decision to bat above him for Victoria in two Sheffield Shield games, which he said hindered his Test selection chances.