Angelo Mathewsmaiden double-century puts Sri Lanka in a near-unassailable position.
West Indies will be touring Sri Lanka in February this year to play three ODIs and two T20Is.
Prithvi Shaw replaces injured Dhawan as India announce squad for ODI series against New Zealand.
Quinton de Kock has been named as the new captain of the South Africa One-Day International side.
Sri Lanka end day three on 295 for 4 and trailing by just 63.
Sri Lanka were 42 for 1 at stumps, after Zimbabwe bowled out for 358 after tea on second day.
England take a 2-1 series lead with an innings-and-53-run victory over South Africa in the third Test in Port Elizabeth.
West Indies chased down 139 in 11 overs after Pollard and Bravo derailed the visitors with three wickets each.
England captain Joe Root takes four wickets as South Africa slip to 102-6, needing further 188 to avoid innings defeat in third Test.
Zimbabwe finished the first day of the first Test against Sri Lanka on 189 for 2 in Harare.