Ashwin picked up his 18th five-wicket haul in Tests as West Indies were bowled out for 196. Rahul scored unbeaten 75 to put India in strong position after Day 1.
India have never won two consecutive Tests in West Indies.
Ashwin picked up seven wickets in the second innings as India defeated West Indies by an innings and 92 runs in first Test.
Mohammad Shami (4/66) and Umesh Yadav (4/41) helped India bundle out WI for 243, Following on, WI ended Day 3 at 21/1, trailing India by 302 runs.
It was memorable day for Virat Kohli, who eased to his maiden double hundred in Tests before R Ashwin (113 off 253) struck his third Test ton.
Virat Kohli had the support of Ravichandran Ashwin (22 batting) at close of play as the two shared an unbeaten 66-run stand.