New Zealand claimed a nervy one-wicket win over Australia at the Cricket World Cup in Auckland on Saturday.

Mitchell Starc (6-28) had threatened to see the visitors to Eden Park to victory with a devastating spell of bowling.

But Australia were unable to defend their paltry total of 151, with Kane Williamson (unbeaten 45) seeing the home side to victory with a huge six over long-on with 161 balls remaining.

Earlier, Trent Boult (5-27) took the spotlight, ripping through Australia's middle and lower order as Australia were bowled out in the 33rd over.

Several of Australia's batsmen made starts but Brad Haddin (43) top-scored with his team going from 80-1 to 106-9.

Brendon McCullum (50 off 24) got New Zealand off to a characteristically fast start before a collapse gave Australia hope, but Williamson led them to victory.

Australia started explosively on the small ground in Auckland before Aaron Finch (14) fell, clean bowled by Tim Southee (2-65) going for another big shot.

Dan Vettori (2-41) came on to bowl in just the seventh over, and he kept it tight to at least slow Australia's momentum.

And the wickets followed.

Shane Watson (23) had settled before pulling Vettori to Southee on the deep mid-wicket boundary.

The next ball saw David Warner (34) fall, trapped in front by Southee before his review failed.

Steve Smith (four) was caught behind and Maxwell (one) chopped on a delivery from Boult to see Australia in all sorts of trouble at 96-5.

And it got worse quickly.

Mitchell Marsh fell for a second-ball duck, leaving his bat hanging outside off stump and also playing Boult onto his stumps.

Clarke (12) was the next to go on his return from a hamstring injury and only a 45-run 10th-wicket stand between Haddin and Pat Cummins gave Australia any chance.

McCullum and Martin Guptill got New Zealand off to a flyer, reaching 39-0 through three overs.

Mitchell Johnson hit McCullum in the forearm, which swelled quickly before a compressive sleeve was applied and the captain continued.

Guptill (11) scooped a catch to Cummins off Starc in the fourth over, but McCullum's dominance continued.

McCullum brought up his 50 off 21 balls, a knock that included seven fours and three sixes.

But he flat-batted a shot straight to Starc off Cummins and when Ross Taylor (one) and Grant Elliott (0) fell cheaply either side of the tea break, Australia had hope.

New Zealand went from 131-4 to 146-9 thanks to Starc, but Williamson belted Cummins back over his head to secure his team's win.