At the tea break, the West Indies still needed 107 runs to save an innings defeat in the first of the two Tests in Sachin Tendulkar's farewell series.
Earlier, Sharma missed out on a double century on debut by 23 runs, while Ashwin slammed his second Test ton in a record 280-run stand for the seventh wicket before India were bowled out for 453 in their first essay.
Ashwin gave the second breakthrough minutes before the tea break when he trapped Kieran Powell from round the wicket with a ball that stayed low and straight.
Powell made 36 off 83 balls (5x4) in his 68-run stand with Darren Bravo, who is batting on three. Shivnarine Chanderpaul was yet to open his account at the tea.
The Eden wicket had little to offer to the bowlers who struggled to get wickets. Besides the odd balls that stayed low and turned sharply, the pitch looked dead as Indian captain M S Dhoni tried out various things. He even gave the ball to the Sachin Tendulkar for a second time in the match.
Continuing his assault, Gayle mistimed a pull shot off Bhuvneshwar Kumar only to get a top edge as Virat Kohli grabbed it.
