Ashwin took 7-71 in the second innings, his best figures overseas, as West Indies were bowled out for 130 in less than 51 overs.
New cap Yashasvi Jaiswal scored 171 for India as the visitors declared their first innings at 5-421 about an hour after lunch for a lead of 271.
That was imposing considering West Indies made just 150 in their first knock.
Offering spin-friendly Windsor Park to two of the world's best spinners was considered overly charitable not long after West Indies won the toss and decided to let India bowl first.
Ashwin, the No.1-ranked Test bowler with a point to prove after being omitted from the World Test Championship final against Australia, and Ravindra Jadeja, the No.1-ranked Test allrounder, padded already impressive statistics with 17 of the 20 West Indies wickets.
Beside 5-60 from the first innings, Ashwin's dozen wickets in the match gave him an eighth 10-wicket haul in a Test, tying Anil Kumble's India record. They are tied for fifth on the all-time list.
Jadeja took 2-38 on Friday for a match haul of five wickets.
The hosts have gone the distance only twice in their last 10 Tests going back 16 months.
India, meanwhile, extended their unbeaten run in the Caribbean to 14 Tests after a seventh win since 2006.
The highest score by an India man on debut was 187 by Shikhar Dhawan in 2013, and Jaiswal looked set to beat it on Friday morning until he fell 16 runs short.
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