Having resumed on 168 for two following on, still 228 shy of making their hosts bat again, Bravo (104no) led the tourists to 235 for four at lunch, although the dismissal of Shivnarine Chanderpaul for just a single was a blow.
The day certainly did not start in positive fashion for the Windies as Marlon Samuels was caught and bowled by Tim Southee in the fourth over of the morning.
When Chanderpaul was trapped lbw by Neil Wagner soon after to leave his side 185 for four it appeared his side could roll over.
But Narsingh Deonarine announced his arrival at the crease with a sweet boundary off Wagner and he proved an able ally to Bravo, who brought up his ton off his 200th delivery with a sweep for four off Ish Sodhi.
By lunch the pair had compiled 50 runs in a conservative but effective partnership, but the tourists remained 161 behind.