A full-strength New Zealand exposed the inexperience of an Australian side missing Ricky Ponting and Adam Gilchrist (both rested), and Andrew Symonds, Michael Clarke and Brett Lee through injury.
New Zealand captain Fleming scored 70 runs from 76 deliveries, while Vincent amassed 73 from 87 balls, with both players hitting eight fours and two sixes in a record opening stand for New Zealand and the first century-stand from a New Zealand opening partnership in 22 years.
Earlier, Bond finished with figures of 5 for 23 from nine and a half overs, taking the scalps of Phil Jacques (1), Brad Haddin (6), Cameron White (13), Brad Hogg (20), and Natahn Bracken (0), in an excellent World Cup warm-up.
Stand-in Australian captain Mike Hussey described the defeat as "demoralising", with the world champions in danger of losing their world number one ranking to South Africa should they lose the Chappell-Hadlee series.
"It's probably as low as we've been or can go," said Hussey, who top-scored with 42 for his side.
"We've got a new group at the moment and we've just got to mould together as quickly as possible."
A jubilant Fleming, who won the crucial toss and sent Australia in to bat first under overcast skies, said man-of-the-match Bond set up the victory.
"It's the best I've seen him bowl for some time and not just because he got five wickets.
"His control was outstanding, and his thought processes were great."
Bad day all round
The visitors' woes were summed up late in the New Zealand innings when Vincent took off his gloves and began walking towards the pavilion, certain he was going to be caught after he top-edged a pull shot off Mitchell Johnson.
But he had to be called back by Fleming as a communication mix-up meant neither the bowler nor the close-in fielder Brad Hodge were able to reach the simple chance.
The second game of the three-match series will be played on February 18 at Eden Park in Auckland, with the final match in Hamilton on February 20.