The match began late by 40 minutes due to technical reasons and later rain spoilt India's chase when they were 15 for none in two overs, chasing 144 to win.
Absence of Super Sopper at the Central Broward Regional Park Stadium meant that the game could not be re-started at cut-off time.
It was heartbreaking for India as their bowlers bowled with supreme control to bundle out West Indies for a mere 143 in 19.4 overs, leaving behind the bashing they had suffered in the opening match.
In the fourth Test at Port of Spain also, the rain and unplayable conditions had denied India the chace to retain their number on rank in Tests as the match ended in a draw.
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Indian bowlers put up a collective effort in restricting the West Indies to a manageable total on a slow wicket that had nothing for the pacers.
Leg spinner Amit Mishra (3/24) provided the opening breakthrough by dismissing Johnson Charles (43) and R Ashwin then combined with paceman Jasprit Bumrah to tighten the noose around the West Indies with regular strikes.
Bumrah (2/26) was consistent with his line and length while Mohammed Shami also chipped in with two scalps.
The Indian pace duo of Bhuvneshwar Kumar and Shami (2/31) initially bowled at a good length but were punished when they strayed as the pitch had nothing to offer for the pacers.
Charles hoicked Bhuvneshwar, who dug one short, for a massive six over mid-wicket to begin the fireworks even as Shami removed the first match centurion Evin Lewis (7).
Charles had no problem whether he was facing a short ball or a length delivery. The strapping Windies batsman dispatched those balls to the boundary ropes with consummate ease.
Mishra struck with his first ball as he saw the back of Charles, who attempted a maximum but found Ajinkya Rahane at long on.
Mishra put the brakes on the scoring rate, giving away only four runs in that over. With spinners looking like making an impact, India captain Mahendra Singh Dhoni introduced left-armer Ravindra Jadeja, who bowled five dots and conceded only one run in the next over.
Jasprit Bumrah had Marlon Samuels (5) caught behind with his first ball while Ashwin had his second wicket when he trapped Kieron Pollard (13) in the next over.
(REOPENS DEL 30)
It was also the first time in the history of Indian cricket that three players -- Ashwin, Jadeja and Jayant -- batting at No 7 or below have scored a half-century each in the same innings.
The next over from the end saw Woakes being removed and Adil Rashid (4/118) being introduced.
Jadeja jumped out at the first opportunity in his bid to loft him for a six but was caught by Woakes at the long-on boundary to miss out on a Test ton.
But Umesh Yadav (12, 42 balls) gave Jayant (55) good company as they added 33 runs to frustrate the visitors further as India crossed 400-run mark and Jayant reached his individual milestone.
The lead came when Jadeja lofted Moeen Ali over mid-off in the last delivery of the 88th over.
Ashwin was looking in fluent touch as he slashed Woakes hard for a boundary between point and cover region. It was followed with another fluent drive as the all-rounder reached 70s.
Finally after India reached 300, Ben Stokes broke the partnership with Ashwin playing a lazy drive to a delivery way outside off-stump only for Jos Buttler to take a low catch.
The Saurashtra all-rounder duly completed his fifty when he pushed Rashid for a single and celebrated it with a customary sword wielding. As if to drive home a point, he flat batted Stokes over mid-on for a boundary.
Young Jayant showed his batting prowess once again as he on drove and square drove Jimmy Anderson before playing a pull-shot off Rashid. He duly competed his half-century in 132 balls.