The Australia skipper smashed 164 off 157 balls, the highest individual One-day International score at the Sydney Cricket Ground, to lead Australia to 324 for eight.
Man-of-the-match Smith struck 14 fours and four sixes in his seventh ODI century after winning the toss to give the Black Caps a tough target to chase down.
Smith then took two great catches and paceman Josh Hazlewood claimed three wickets to dismiss the Kiwis for 256 in 44.2 overs.
Smith’s knock, the seventh highest by an Australian, surpassed South Africa’s A.B. de Villiers’ 162 at the same ground in last year’s World Cup.
It was also the joint-highest by an Australia captain. Ricky Ponting also made 164 against South Africa in Johannesburg in 2006.
He then underlined his man-of-the-match qualities with two decisive catches in the Black Caps’ innings.
It was his throat-high catch at slip that got a big breakthrough to dismiss New Zealand skipper Kane Williamson for just nine.
Smith later latched onto a flying one-handed screamer to dismiss B.J. Watling for six off Mitchell Marsh, hurling himself to his left in the gully for a stunning catch.
“I got a bit of luck. I was probably out lbw at one point,” Smith said. “It’s nice to get my highest score at my home ground and post a huge total.
“We were able to get over the line, which was the most pleasing thing. I am sure New Zealand will hit back hard.”
Opener Martin Guptill raised his 11th ODI century with a mighty six off Marsh over long-on off 93 balls and was his side’s major hope of reeling in Australia’s huge target.
But leg-spinner Adam Zampa coaxed Guptill into a false shot to find fielding substitute Glenn Maxwell at mid-wicket and he was on his way for 114 off 102 balls in the 33rd over.
“Guptill’s was fantastic hundred — one of his better hundreds — and gave us a chance,” Williamson said. “If we reflect back, we bowled poorly in the middle stage. I think we were good in patches, and not so good in some, which left us a tall total to chase.”
Jimmy Neesham put on 92 runs for the third stand with Guptill before he holed out to Hazlewood off Mitchell Starc in the 22nd over.
Smith’s top-ranked team suffered a 5-0 ODI series drubbing in South Africa in October and earlier looked shaky again when reduced to 92 for four in the 21st over.
But Smith, who could have been out three times, flailed the Black Caps’ bowlers and put his side in the ascendancy. 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 wicket-keeper Matt Wade clobbered three sixes off a Jimmy Neesham over on his way to 38 off 22 balls.
Smith gave New Zealand two chances in Boult’s third over.
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.
Head put on 127 for the fifth wicket with Smith, before he was caught and bowled low down by Boult.
D.A. Warner b Ferguson 24 A.J. Finch b Henry 0 S.P.D. Smith c Munro b Boult 164 G.J. Bailey c Watling b Neesham 17 M.R. Marsh run out 1 T.M. Head c and b Boult 52 M.S. Wade b Henry 38 P.J. Cummins not out 0 M.A. Starc c Watling b Neesham 11 A. Zampa not out 2
EXTRAS (LB-1, W-9, NB-5) 15
TOTAL (for nine wkts, 50 overs) 324
FALL OF WKTS: 1-1, 2-47, 3-89, 4-92, 5-219, 6-302, 7-311, 8-322.
DID NOT BAT: J.R. Hazlewood.
BOWLING: Henry 10-0-74-2 (1nb, 1w); Boult 10-1-51-2 (2w); Ferguson 9-0-73-1 (4nb, 2w); de Grandhomme 6-0-27-0; Santner 9-0-40-0; Neesham 6-0-58-2 (4w).
M.J. Guptill c sub (Maxwell) b Zampa 114 T.W.M. Latham b Hazlewood 2 K.S. Williamson c Smith b Hazlewood 9 J.D.S. Neesham c Hazlewood b Starc 34 B.J. Watling c Smith b Marsh 6 C. Munro c Bailey b Cummins 49 M.J. Santner c Warner b Zampa 0 C. de Grandhomme lbw b Hazlewood 6 M.J. Henry c Bailey b Cummins 27 L.H. Ferguson b Marsh 0 T.A. Boult not out 1
EXTRAS (LB-4, W-4) 8
TOTAL (all out, 44.2 overs) 256
FALL OF WKTS: 1-3, 2-34, 3-126, 4-140, 5-185, 6-187, 7-203, 8-253, 9-255 .
BOWLING: Starc 7-1-37-1; Hazlewood 10-0-49-3 (2w); Marsh 8.2-1-38-2 (1w); Cummins 9-0-62-2 (1w); Zampa 10-0-66-2.
RESULT: Australia won by 68 runs to lead three-match series 1-0.
UMPIRES: M.D. Martell (Australia) and H.D.P.K. Dharmasena (Sri Lanka).
TV UMPIRE: P. Wilson (Australia).
MATCH REFEREE: R.B. Richardson (West Indies).
MAN-OF-THE-MATCH: Steve Smith.
SECOND MATCH: Canberra (D/N), Tuesday.
THIRD MATCH: Melbourne (D/N), Friday.