At stumps, KC Brathwaite at 53 not out in 143 balls and DM Bravo 18 out of 66 balls were at the crease in 47 overs, still trailing India by 247 runs.
India, however, got a breakthrough in the 24th over when off opener LR Johnson was run out for 23 in 75 balls by a quick throw at the non-striking wicket by KL Rahul when Windies score was 59 in 24th over.
India's three pacers -- Mohammed Shami, Bhuvaneshwar Kumar and Ishant Sharma -- and two spinners Ashwin and Ravindra Jadeja contained the openers with line and length, but did not succeed in getting early wickets at the end of the day's session.
In the sixth over, Johnson was dropped in the second slip by Jadeja
Shami was also unlucky to get the first wicket when Rahul dropped a touch catch by Johnson in the sixth over when the score was 12 for none.
Earlier, Windies bundled out India for 353-run in 129.4 overs.
Surviving the nervous nineties for too long and after getting stuck at 99 for six overs, Ashwin crossed the 100-mark in style by lofting a Roston Chase ball to six at long off in the 117th over of the innings, taking the score to 323 for 5 wickets.
This is Ashwin's second Test century in this series after 113 in the first Test at Antigua on July 20 and fourth against the Windies.
Three overs later, Saha too hit his maiden Test hundred with two runs of a Chase ball to the cover drive in the 121st over, taking the overall score to 332 for 5.
Incidentally, Saha is the fourth Indian wicket-keeper after Vijay Manjrekar, M.S. Dhoni and Ajay Ratra to hit a Test century in the away from home series.
In the following over (122), Saha nicked the ball from Alzarri Joseph to be caught by stumper Shane Dowrich for 104 in 227 balls with 13 boundaries, which is the highest in this innings.
Ashwin's sixer is the only one in the Indian innings. His marathon innings ended on a high note of 118 runs in 297 balls with six boundaries.
The centurion duo also set a record 213-run partnership for the sixth wicket against the Windies.
With the star middle order batsmen back in the pavilion, the tail-enders did not last long after Jadeja left for 6-run, caught behind by keeper Dowrich of a Cummins' ball, as Bhuveneshwar Kumar and Ishant Sharma got out for ducks, while Mohammed Sami remained not out with nil score. India lost its last 5 wickets for a paltry 37-run.
For the hosts, keeper Dowrich took four catches, while ML Cummins and debutant Alzarri Jospeh shared three wickets each, followed by ST Gabriel and Chase two each. Skipper Jason Holder and Kraigg Brathwaite did not get any wicket.
With a record double century partnership, Ashwin and Saha pulled India out of deep trouble on the first day defying the Windies attack and taking the score to 339 from 126 for 5 wickets on Tuesday after Ajinkey Rahane left for 35 runs.
Windies began their chase with openers Brathwaite and Johnson surviving the initial bust of Indian pace attack, which was aided by seam and swing.
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