The rain though had the last laugh as the match was called off without a result being possible.
Thursday's first match of this year's edition saw hosts England beat Bangladesh by eight wickets at the Oval in another Group A clash.
After failing to win a game in their trophy defense in 2013, Australia intend to regain the championship by blasting all-comers.
New Zealand captain Kane Williamson raises his bat after reaching his century at Edgbaston.More news: Osinbajo Excitement as Acting President visits Calabar
Williamson's ninth one-day global ton was a typically assured knock, featuring eight fours and three sixes before he was run out in the 40th over.
Josh Hazlewood was the chief beneficiary as several batsmen carelessly holed out, with the fast bowler returning one-day worldwide best figures of six for 52.
Smith was particularly displeased with the bowling effort of his pacers early on in the New Zealand innings. "We had work to do and a quality bowling attack against us, so we perhaps got away with one there".
But Ronchi scrambled into the crease after after Matthew Wade made a awful hash of gathering Mitchell Starc's throw towards the stumps.
Josh Hazzlewood ran through New Zealand's lower-order and returned with impressive figures of six for 52 from his nine overs.
Williamson underscored his status as one of the players to watch in this tournament, easing into his 97-ball innings before splattering Australia's much-feared pace attack around Edgbaston with an array of shots.
Alongside Ross Taylor (46), he put on 99 for the third wicket.More news: Cristiano sings 'Ronaldo, Ballon d'Or' as Madrid celebrate Champions League triumph
Josh Hazlewood was the pick of the Australian bowlers, finishing with 6-52, but Smith was unhappy with what was sent down for the first 40 overs as Kane Williamson scored a fine century before his run out for 100 sparked a stunning late collapse.
Starc bowled yet another quick over however was hit for four of the second ball by Ronchi. Trent Boult survived the hat-trick but was then caught behind next ball.
John Hastings - who has plenty of English county experience - was chosen over paceman James Pattinson.
Ronchi set the tone with 65 off 43 balls.
"Guys were a little bit concerned at the time, and didn't really know what to do", the Australia captain said.
Left-arm fast bowler Starc, arguably the world´s leading ´yorker´ bowler, has recovered from a foot injury that cut short his tour of India.
New Zealand were on course for a score well above 300 while Williamson was at the crease in an innings reduced from the ODI standard 50 to 46 because of rain. "This is a big tournament; we pride ourselves on how we perform in these tournaments". Earlier in their innings, Australia's only decent bowling came from the combined fifth bowler of Head and Henriques, who conceded 47 in their 10, their most frugal in the game.More news: Oregon tops LSU 4-1, will play Oklahoma in WCWS semifinals