Five-time champions Australia are back on track for a last-four spot having won four matches on the trot after an unimpressive start which saw them lose their first two games.
Travis Head smashed 109 off 67 balls in his first World Cup game and added 175 runs for the opening wicket with David Warner (81 off 65 balls).
Glenn Maxwell (41), Jos Inglis (38) and Pat Cummins, who blasted 37 off only 14 balls, upped the ante towards the end.
Glenn Phillips did an admirable job with the ball, ending with figures of 3/37 as his colleagues were taken to the cleaners.
With the bat, centurion Rachin Ravindra top-scored for New Zealand with a counterattacking 116 off 89 balls.
Brief scores:
Australia: 388 all out in 49.2 overs (Travis Head 109, David Warner 81; Glenn Phillips 3/37)
New Zealand: 383/9 in 50 overs (Rachin Ravindra 116, Jimmy Neesham 58, Josh Hazlewood 2/70).