New Zealand lead the series 2-0 after taking the first Test by 27 runs and the second by 10 wickets.
McLean Park promises a juicy, hard pitch after sweating under the covers following days of rain in Hawke's Bay and should produce a result, weather permitting.
A damp outfield has already forced a four-and-a-half hour delay on the first day, with play set to start at 3:00pm (0300 GMT).
Fine weather is forecast for the rest of the weekend with rain expected again on Monday.
New Zealand's prospects have been boosted by the return of spearhead bowler Shane Bond from illness to a pace attack that claimed 17 wickets in the second Test, while West Indies frontline quick Fidel Edwards is carrying an injury.
Bond's return is at the expense of Kyle Mills who took six wickets in the second Test.
West Indies captain Shivnarine Chanderpaul said their full squad was available for selection despite nagging niggles to Edwards.
For New Zealand captain Fleming it will be his 75th Test as captain, putting him outright second in the all-time list behind Australian Allan Border on 93.
New Zealand: Jamie How, Hamish Marshall, Peter Fulton, Stephen Fleming (captain), Nathan Astle, Scott Styris, Brendon McCullum, James Franklin, Daniel Vettori, Shane Bond, Chris Martin.
West Indies: Daren Ganga, Chris Gayle, Runako Morton, Brian Lara, Shivnarine Chanderpaul (captain), Dwayne Bravo, Dwayne Smith, Denesh Ramdin, Daren Powell, Ian Bradshaw, Fidel Edwards.
Umpires: Mark Benson (ENG), Ian Powell (RSA).
Match referee: Mike Procter (RSA).