Ashwin produced an off-spin bowling masterclass and triggered a second-innings slide that saw the hosts collapse from 88/2 to 132/8 on the fourth and penultimate day.
A defiant ninth-wicket stand of 95, West Indies' highest in the game, between Carlos Brathwaite (51 not out) and Devendra Bishoo (45) delayed the inevitable before Ashwin came back to seal the issue by bowling the hosts out for 231.
India bowled out the West Indies for 243 in their first innings, having amassed 566 for eight declared after opting to bat. Forced to follow-on after conceding a massive lead of 323, the hosts failed to cope up with intense pressure created by Ashwin and Co on a pitch that offered assistance to slow bowlers.
At the Sir Vivian Richards Stadium, the visitors shot out the hosts in three hours over the post lunch and tea session to finish their two innings at 243 and 231.
Post lunch, it was an extended session of play which proved enough for India to force a win. But first they had to break through the 67-run partnership between Rajendra Chandrika (31) and Marlon Samuels (50). The two batsmen began again in the same vein, trying to play for time, and in doing so, the latter crossed the 50-mark off 74 balls raising hopes of a fight back.
In the very next over, he removed Jermaine Blackwood (0) for a second duck in the match, with skipper Virat Kohli holding a magnificent diving catch at midwicket to aid in the dismissal.
(REOPENS FGN 44)
Four overs later, Ashwin had Roston Chase (8) caught at forward short leg and the West Indies' resistance was more or less over.
India then looked to wrap up the innings quickly, but a sedate 69-run stand for the ninth wicket between Brathwaite and Bishoo thwarted their efforts to wrap up the match before tea. The duo played some attacking strokes and brought up the 200-mark going into the break.
The morning had begun with overnight batsmen Chandrika and Darren Bravo (10) looking to play on for time as well as score runs whenever possible. India started the proceedings with Ishant Sharma (1-27) and Umesh Yadav (1-34), the duo looking sharp and bowling fuller deliveries, especially the former who was a marked improvement from his first innings' outing.
And this brought immediate success as Yadav sent back Bravo off the fifth ball of the day, as Ajinkya Rahane dove to his left and held a two-handed catch at gully. The duo bowled a consistent spell thereafter, testing both Chandrika and Samuels, but the batsmen showed enough resilience to stay put at the wicket.
Mohammed Shami (0-26) was soon introduced into the attack, and he was on the money straightaway.
Ashwin could have had a wicket too, towards the end of the session as Shane Dowrich edged to Rahane at slip, but the ball was seen to have bounced on replay. Jason Holder was the other unbeaten batsman.
Earlier, West Indies reached 90/3 at lunch after Brathwaite had defied the Indian bowlers along with Devendra Bishoo (12). The duo put on 38 for the second wicket but more importantly frustrated the visitors by batting out 17.5 overs.
Samuels raced on quickly thereafter and looked more comfortable at the crease as time passed, as did Chandrika at the other end.
About 40 minutes were left for lunch when rain intervened and cut short the session. Despite the shower passing by, the umpires called for an early lunch to allow for the ground staff to prepare the field for resumption.
Chandrika's dismissal four overs after the lunch break, taken early due to a short spell of rain, triggered a slide from which the hosts failed to recover.
The opener's dismissal was followed by those of Jermaine Blackwood, who had a pair in the match, Samuels, debutant Roston Chase, Shane Dowrich and skipper Jason Holder as West Indies slumped to 132 for eight.
