Kane Williams scored a fine century as New Zealand posted 291 all out in 45 overs, a total that at one stage looked like being much higher before seamer Josh Hazlewood recorded career-best figures of 6-52 for Australia.
Rain in the interval between innings meant Australia faced a reduced victory target of 235 from 33 overs, and they limped to 53 for three in nine overs before the heavens opened for a final time and the game was abandoned.
Hosts England top the pool with two points, New Zealand and Australia have one each, and Bangladesh are on zero.
Williamson’s 100 off 97 balls anchored a New Zealand innings that promised a lot more, but Australia found their groove in the closing overs to take the final seven wickets for 37 runs.
Williamson put on 77 with opener Luke Ronchi (65) and 99 for the third wicket with Ross Taylor (46) before he was run out the ball after reaching his ton.
New Zealand were 254-4 with 10.5 overs remaining and on course for a score well in excess of 300, but Hazlewood induced a number of false strokes from the New Zealand batsmen.
Glenn Maxwell took four catches, one short of Jonty Rhodes’s one-day international record for a fielder of five.
Tight New Zealand bowling at the start of Australia’s reply built pressure.
They lost the key wicket of David Warner (18) caught behind by wicketkeeper Ronchi off Trent Boult, before Adam Milne dismissed Aaron Finch (8) and Moses Henriques (18) with the last ball before rain stopped play for a final time.
(Reporting by Nick Said, editing by Ed Osmond)
