Mitchell Starc dropped him on 54, denying Pat Cummins payback for a costly opening spell, but Hastings' gentler seamers eventually did the trick.
Earlier, Ronchi - born in New Zealand but raised in Australia, for whom he played seven limited-overs internationals in 2008-09 - provided some entertainment with three sixes and nine fours in a 43-ball salvo as a pinch-hitting opener.
Smith accepted the weather had probably spared his side a damaging defeat, saying: "We still had a lot of work to do and they've got a quality bowling attack as well, so we perhaps got away with one there".
As the Australian's had not faced 20 overs, the two points available for a win were split between the sides.
Subsequently, both sides picked up a point, and Smith's men now have to beat Bangladesh at The Oval on Monday to have any genuine chance of progressing to the semi-finals.
New Zealand, on the other hand, can be argued as favourites after playing ODI series against Ireland and South Africa.
Just when three bowls were bowled in the tenth over as the skipper introduced Hastings, rain interrupted the play at Edgbaston, Birmingham.
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Although they pulled things back later on, Australia captain Steve Smith, celebrating his 28th birthday on Friday, slammed his side's bowling effort.
New Zealand were a World Cup finalist in 2015, and World Twenty20 semifinalists in 2016, and have developed a thick skin, like captain Kane Williamson.
His fellow opener, Aaron Finch fell to Adam Milne in the next and after hitting four fours in his 16-ball knock, Moises Henriques was next to go - a thick inside edge onto his pad giving Milne a simple return catch.
Williamson notched up his ninth ODI ton as he scored exactly 100 from 97 deliveries.
In five innings against Australia Latham's only got to double figures once while Ronchi's highest total is 19 in six innings.
Australia were in trouble at 53/3 after nine overs before rain came calling and covers were brought on.
Keeping the English conditions in mind, it is important that the Australian pacers don't lose control, as the batsmen can easily use the lightning quick outfield to their advantage by using the pace of the ball.
"For us it´s trying to attack it as best we can". Williamson had got his eye in and started to pepper the fence around the ground, while Taylor, too, showed he was setting himself up for the big one.
The Black Caps didn't quite manage it, and they would have wanted more especially after Williamson and Taylor put on 99 for the third wicket.