Sharma was dismissed for a marathon 177 and Ashwin contributed 124 as India’s first innings ended at the stroke of lunch on the third day at the Eden Gardens. The duo added a record 280-run partnership for India for the seventh wicket.
For the visitors, Shane Shillingford was the most successful bowler, returning figures of six for 167 in 55 overs.
Resuming at overnight 354/6, India scored 99 runs for the loss of four wickets in the first session. Sharma added 50 runs to his overnight unbeaten knock of 127 while Ashwin, who started the day on 92, managed 32 runs before he was bowled by Shillingford.
Sharma, after spending a little over six hours in the middle, was trapped in front of the wicket by Veerasammy Permaul. The 26-year-old Mumbaikar smashed 23 fours and a six, while Ashwin found the fence 11 times.
The West Indies triggered a collapse after Sharma’s dismissal as India lost their remaining four wickets for 17 runs.
Sharma also became the second Indian after Shikhar Dhawan to score a 150 on debut.
Sharma padded a straighter one on the offstump from leftarm spinner Permaul to be adjudged lbw by umpire Richard Kettleborough.
It was a huge relief for the Indies who had been struggling to break the partnership that began midway into the second session yesterday.
Ashwin, too, did not last long and his career best innings came to an end after being bowled around the legs by Shillingford, who grabbed his fifth five-wicket haul in Tests.