Resuming the day at 234 for five, India took control of the game in what was a second consecutive wicketless session for the West Indies.
The visitors have the upper hand in the game largely due to the efforts of Ashwin (99*) and Saha (93*), who batted out another session to stretch their partnership to 190 runs. India scored 82 runs in the two hours of play with 25 overs being bowled.
Saha got to his third Test half-century off 135 balls, and thereafter India's 250-mark came up in the 97th over. But the two batsmen were still not looking to get on with the scoring rate as they looked to settle down and play a long innings that would give their team the upper hand once again.
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Roston Chase (2-50) meanwhile persisted with his leg-stump line, bowling to a predominantly leg-side field to Ashwin, and thus looking to dry up the runs. The two batsmen didn't mind as only 21 runs came in the first hour of play spanning 13 overs. However in the second hour, the scoring rate finally picked up a bit as a more-confident Saha played some fine shots.
He wasn't too aggressive, but looked positive against the pacers and looked to attack Chase whenever possible, as he quickly caught up in the nervous 90s with his teammate.
Saha's eagerness meant that 51 runs came off the last 10 overs going into the lunch break. But neither of the two batsmen could then go on to score their respective hundreds surprisingly enough, even as 82 runs came in this morning session.
Latham, at the other end, edged Ashwin for a four and then struck the off spinner - when he bowled short - for two more fours in the 29th over to bring up the team's 100.
The left-handed opener then reached his own half ton, the third one for him in the series, with a swept four off Jadeja - his seventh hit to the fence -off the 95th ball he faced.
Latham survived a close call off Jadeja when he swept the left arm bowler only for the ball to take the inside edge and strike his boot on the full before ballooning to short gully fielder Rahane, but umpire Bruce Oxenford denied the Indians the wicket by turning down the concerted appeal.