Besides Voges, stand-in skipper George Bailey contributed a patient 55 off 91 balls, his second consecutive half-century.
However, it was Glenn Maxwell's cameo towards the end that propped up Australia's run rate and took the score past 240. Maxwell remained unbeaten on 29 off 22 balls and hit two sixes and a four. He added 24 runs of a mere 14 balls with Clint Mckay for the ninth-wicket.
As far as specialist batsmen were concerned, Voges and Bailey were the ones to have made noteworthy contributions for Australia, who desperately need a win to keep their chances of securing a semifinal berth alive.
Mitchell McClenaghan was the most successful bowler for New Zealand, returning with figures of four for 65 in 10 overs, his second such haul after his effort in the win against Sri Lanka on Sunday. Nathan McCullum picked up two for 46.
Sent into bat, Australia were off to a disastrous start as they lost two wickets, including the important one of Shane Watson, with just 10 runs on the board.