West Indies trailed by 197 runs with three wickets remaining when drinks were called in the second session on the fourth and penultimate day.
Faced with the improbable task of scoring over 300 runs in their second innings to make India bat again, West Indies collapsed under intense pressure created by Ashwin and Co on a pitch that offered assistance to the slow bowlers.
Ashwin ran through the West Indies batting line-up, picking up 4/41 in 16 overs, after Marlon Samuels (50) and Rajendra Chandrika defied India in the first session with a 67-run partnership for the third wicket.
The opener's dismissal was followed by those of Jermaine Blackwood, who had a pair in the match, Samuels, debutant Roston Chase and Shane Dowrich as West Indies slumped to 120 for seven.
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Earlier, a short rain shower stopped India's march as the hosts went into an early lunch at 76 for two at the Sir Vivian Richards Stadium.
The morning began 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 (1-17) and Umesh Yadav (1-19), the duo looking sharp and bowling fuller deliveries, especially the former who was a marked improvement from his first innings' outing.
Samuels in particular looked aggressive and used good hand-eye co-ordination to smack nine boundaries in the session. The two batsmen put on 50 off 98 balls, while the West Indies' score crossed the 50-mark in the 27th over.
Mohammed Shami (0-20) was soon introduced into the attack, and he was on the money straightaway.
About 40 minutes were left for lunch when rain intervened and cut short the session.
Yesterday, Mohammed Shami and Umesh Yadav shared eight wickets to bowl the hosts out for 243 runs and enforce the follow-on thereafter. India amassed 566 for eight declared in their first session.