In a match reduced by rain to 46 overs per side, the Blackcaps were on course for a score well above 300 while Williamson was at the crease during well-judged innings of exactly 100.
The rain returned during the lunch break, further reducing the game to 33 overs per side with a revised target of 235 for Australia.
But his run out sparked a slump that saw the Blackcaps dismissed for 291 after losing their last seven wickets for 37 runs in 35 balls.
Josh Hazlewood was the chief beneficiary as several batsmen carelessly holed out, with the fast bowler returning one-day international best figures of six for 52.
Hazlewood took three wickets in four balls to wrap up the innings with an over to spare.
The Blackcaps made a brisk start either side of a rain break after Williamson won the toss and, surprisingly, opted to bat in overcast conditions.
Luke Ronchi led the way with a dashing 65 that saw him launch Pat Cummins high over long-off for six.
Australia had opted against fielding all four of their out-and-out fast bowlers, with James Pattinson the man who missed out on Friday.
Cummins, however, had already proved expensive by the time rain stopped play with New Zealand 67 for one midway through the 10th over.
The players were off the field for nearly two hours and when they returned, Ronchi carried on in a 15th over, bowled by Cummins, that yielded 15 runs.
The third ball was crashed through the covers for four by Ronchi, who should have been out for 54 when the next delivery saw him miscue a pull only for Mitchell Starc to drop the catch at mid-on.
Ronchi celebrated by flat-batting a four before ending the over with a soaring straight six.
Cummins’s first five wicketless overs had cost 52 runs.
John Hastings, however, restored some order for Australia when Ronchi found Glenn Maxwell at point to end a 43-ball innings featuring nine fours and three sixes.
New Zealand were now 117 for two in the 16th over after a stand of 77 in 60 balls between Ronchi and Williamson.
Williamson showed touch play could be effective too when he swept off-spinner Travis Head for a four between two legside fielders.
Alongside Ross Taylor, he put on 99 for the third wicket before his experienced team-mate fell for 46 when he holed out to mid-off against Hastings.
Williamson, however, hoisted Hastings for a legside six to go into the 90s before a flicked four and driven single off the same bowler saw him to a 96-ball century, his ninth at this level, with eight fours and three sixes.
His second fifty came off just 34 balls.
But he was then run out going for a sharp single by Moises Henriques’s throw to Cummins.
Hazlewood dismissed tailenders Adam Milne and Mitchell Santner as they went for big hits. Trent Boult survived the hat-trick but was then caught behind next ball. – AFP