The hosts reached 90 for three at lunch, still trailing by 476 runs in reply to India's mammoth first innings total of 566 for eight declared.
At the Sir Vivian Richards Stadium, Kraigg Brathwaite (46 batting) defied the Indian bowlers along with Devendra Bishoo (12), as the duo put on 38 for the second wicket but more importantly frustrated the visitors by batting out 17.5 overs.
Starting at their overnight score of 31/1, Bishoo looked to stay with his partner for as long as possible, and he was successful in achieving that goal. He frustrated the Indian bowlers for nearly 70 minutes, and in this interim, saw off the likes of Ishant Sharma (0-24), Umesh Yadav (0-12) and Shami (2-23) without much discomfort.
At the other end, Brathwaite was happy to leave as many deliveries as possible, and he was helped by the wide deliveries bowled at him by the Indian pacers. When the spin came on, he looked to attack R Ashwin (0-22) and didn't allow the lead spinner to settle down at all, hitting him for boundaries in successive overs.
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Bravo (11) then came to the crease, and he looked solid there albeit only for a short while. Kohli changing around his bowlers too quickly perhaps helped him in this endeavour, particularly the pacers who all bowled short spells from the Sir Curtly Ambrose End. Ishant and Umesh were taken off after one and two over spells respectively, and then Shami came on to bowl.
Warner was also lucky to be bowled off a no-ball by Jayant when on 16.
Ashwin, on the other hand, was not only turning the ball but also kept down the runs with Warner, especially, in no mood to try and attack the home team's spin trump card.
Ashwin, who conceded a four to Renshaw with a poor ball on the batsman's pads in his first over, kept the lid on the run-rate from then on and also bowled three maiden overs in a row before switching over to the pavilion end after a first spell of 8-4-10-0.
Warner, who was initially outscored by his opening partner, soon got past that phase by striking Jayant for a couple of fours in two overs, forcing India captain Virat Kohli to bring on third spinner Ravindra Jadeja.
With every over, Renshaw grew in confidence in his first innings in India.
The tall England-born Renshaw then got past his partner's score again as he first tickled a ball from Ashwin to fine leg for a boundary.
Warner, on 37, had two close calls. He first survived a big leg before shout from Ashwin and then nearly popped up a return catch to the off-spinner in the same over.
Just when the Indians were getting frustrated, Kohli decided to replace the unimpressive Jadeja with Umesh and the fast bowler struck in his very first over, the 28th of the innings, by making Warner chop a ball on to the stumps.