Vincent blasted 102 off 117 balls to register his second One-day international hundred while Astle cracked 81 off 88 deliveries and Fleming belted 67 off 59.
Chris Gayle captured three wickets for 50 runs from his 10 overs for the West Indies while Ian Bradshaw and Dwayne Smith collected one wicket each but not before the New Zealand top-order had wreaked havoc with the bat.
Vincent struck 10 boundaries and a six to reach his second ton after making 172 against Zimbabwe in Bulawayo last August while Astle hit four fours and three sixes to follow up his century from Saturday's third match in Christchurch.
Fleming was also in an aggressive mood, slamming six boundaries and four sixes as he and Vincent put on 106 in 19 overs for the opening wicket after West Indies had won the toss and sent the home team in to bat.
The West Indies, beaten in each of the first three matches of the series, briefly put the brakes on New Zealand's scoring when they dismissed debutant Ross Taylor (15), Scott Styris (five) and wicketkeeper Brendon McCullum (21) but not before the serious damage had already been done.