On a day when the tourists relied heavily on debutant spinners Taijul Islam and Shuvagata Hom on a placid pitch at the Arnos Vale Stadium in St Vincent, Brathwaite's unbeaten 123 off 269 deliveries (eight fours) reflected the 21-year-old's unflappability in almost any circumstances.
The rookie opener put on 116 for the first wicket with Chris Gayle (64) to make Mushfiqur Rahim regret his decision to put the West Indies in to bat on winning the toss at the start of the day.
Darren Bravo joined in the steady accumulation of runs following the comparatively swift dismissal of Kirk Edwards, contributing 62 to a 128-run third-wicket partnership before a careless off-drive off Taijul offered a simple catch to Mahmudullah at mid-off.
Shivnarine Chanderpul, who took 183 off the Bangladeshis playing for a St Kitts Invitational XI in a three-day match in Basseterre the previous weekend, will resume on the second morning with Brathwaite after the heaviest, most sustained rainfall of the day brought an early end to play.
He did enjoy a moment of luck though after reaching three figures, Mushfiqur failing to hold on to an outside edge behind the stumps off the bowling of Shuvagata.