Bravo, who made 58 and 80 in the first two Tests, cracked nine fours in his 111-ball knock to steady the innings after the first-ball dismissal of former captain Chris Gayle.
He put on 115 for the second wicket with opener Devon Smith, who hit a solid 55 before being trapped leg before by unorthodox spinner Ajantha Mendis in the final session. Smith hit seven fours in his fifth Test half-century.
Only 40 overs were possible in the day due to bad light and rain.
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