Rahane reached his 8th Test fifty off 88 balls in the penultimate over of the day, and at stumps, they had added 85 runs for the 4th wicket, as India looked to press matters and force a result on day five.
Kohli went cheaply in India's second innings, trapped lbw by Miguel Cummins for four after making just three in the first knock.
India vs West Indies 3rd Test is scheduled for a 7:30 pm IST (10 am local time) start.
There was a good chance that you might be nicked off or you might get a good ball any time. When the lunch van pulled up, Ashwin was unbeaten on 99 and Saha 93. And while they succeeded in doing so, there were quite a few hiccups along the way.
Ishant Sharma removed Bravo (29) with a well directed bouncer before Ashwin had Brathwaite (64) caught down the leg with a ball which spun a mile.
In the very next over, on 26, Ashwin was nearly caught at forward short leg, the ball just dropping short, with Roston Chase (2-38) the unlucky bowler.
Ravichandran Ashwin joined the carnival with the wicket of Cummins, but it was fitting for Bhuvneshwar to end the innings, although he had to wait for his fifth scalp after two catches went down. Fortunately for him, though, Shane Dowrich was in an obliging mood, jabbing at a ball that he should have left well alone, spearing an edge to Shikhar Dhawan, who parried the ball at slip but managed to hold on.
Bhuvneshwar Kumar undermined the West Indies batting with figures of 5 for 33.
Bhuvneshwar, out of nowhere, got his rhythm back and as soon as he did so, ran through the West Indies middle-order.
Saha's wicket breathed life back into the West Indies quicks and before you knew it, Brathwaite and Johnson were padding up to open the batting. He bowled six maidens and conceded 16 runs.
With a lead of 128, India's batsmen came out with a strong positive intent. Then, in the first innings, he got out for 9 after looking to have played himself in.
And that too with the additional loss of a wicket as Chase bowled Rahane in the 50th over, the batsman completely misjudging the flight.
"We've got to be a little more patient, put a bigger price on our wickets".
Regional cricket fans have become accustomed to spectacular West Indies' collapses. Cummins in his second Test match took 3/54, Joseph on debut 3/59 while Shannon Gabriel (2/80) and Roston Chase (2/70). were the other wicket takers. Kumar and Shami had started off proceedings, and the duo was right on the money with the new ball. Today they were pitiless with the ball.
Surprisingly then, skipper Kohli (3) came out to bat and was tested immediately with a mix of short and moving deliveries. He bowls to Dowrich outside the off stump and he nicks it to first slip to Dhawan.
India's glimmer of hope was lit in the ninth over of the morning when Ishant Sharma, with some help from the third umpire Gregory Brathwaite, who felt Sharma's foot had landed inside the crease when replays suggested otherwise, dismissed Darren Bravo.
West Indies were in trouble at 4 for 2 and needed their experienced pair of Marlon Samuels and Darren Bravo to step up.