After an early morning collapse in which the West Indies slumped to 185-4, the defiant Bravo restored order with a controlled performance to pass the 100 mark for the fifth time in his career and be not out 210 at stumps. (Agencies)
The 24-year-old left-hander added 122 with Narsingh Deonarine for the fifth wicket and 56 with Ramesh Ramdin for the sixth.
By the the close of the fourth day he was sharing an unbroken 80-run stand with captain Darren Sammy on 44 and ensured New Zealand would have to bat again.
The West Indies were forced to follow on after being all out in their first innings for 213 in reply to New Zealand's 609-9 declared.
They resumed the fourth day at 168-2 and lost two quick wickets before producing the tempered performance that was missing in their first turn at bat.
Marlon Samuels was first to fall for 23, caught and bowled by Tim Southee, and four overs later Neil Wagner picked up the prized wicket of Shivnarine Chanderpaul for one.
It was the second time in the match the West Indies senior batsman had been trapped leg before wicket by a left armer after falling to Trent Boult in the first innings.
But after claiming the quick pair of wickets, the New Zealand bowlers lost penetration on a lifeless wicket and the new ball did not bring the sting they wanted.
Their cause was not helped either by the few missed catch opportunities offered Bravo and Deonarine as they ate into the formidable target. A drive from Deonarine, on 40, went straight to Brendon McCullum at short cover who made two attempts to grab the ball before it spilled to the ground.
But shortly after reaching his fifth half-century, Deonarine edged Corey Anderson to wicketkeeper BJ Watling who made no mistake.
Bravo, who survived a caught and bowled chance to Neil Wagner when on 82, remained a rock in the middle and with the dismissal of Deonarine he found another willing partner in Ramdin.
Ramdin reached 24, including four fours, before he failed to read an Ish Sodhi googly which nipped between bat and pad.
It was then up to Sammy to continue to support Bravo as he headed unflinchingly past his previous highest score of 195 set against Bangladesh two years ago.
Despite being hampered by a leg muscle injury, Sammy had no trouble lashing out as he blasted five boundaries and two sixes in his 44.
Bowling for New Zealand, leg spinner Sodhi has two wickets while Southee, Boult, Wagner and Anderson have one each.
After an early morning collapse in which the West Indies slumped to 185-4, the defiant Bravo restored order with a controlled performance to pass the 100 mark for the fifth time in his career and be not out 210 at stumps.