From 45 for 3, there was not much resistance as Hope was snapped when he played a Ravindra Jadeja delivery for the turn to give Rahane his second catch.
He followed it up with a quickfire 70 in the first innings of the second Test in Hyderabad.
Yadav continued breathing fire on a pitch that offered very little for the bowlers.
India lifted their 10th consecutive win at home by the end of Day three of the second Test here at Rajiv Gandhi International Stadium on Sunday.
India vs West Indies - Highlights & Stats
In a space of 16.1 overs, India lost five wickets for 25 runs to move from a comfortable 314 for 4 to 339 for 9 before Ravichandran Ashwin (35 of 83 balls) made a useful contribution.
Yadav has been in red hot form in the recently-concluded two-match Test series against the Caribbean outfit, where he became only the third Indian quickie to have a 10-wicket haul. "India is (the) number one team in the world and we expected to be pushed by them", said Holder. The credits, however, go to the cricketers who had played in the past and raised the standard of Indian cricket to the level it has reached today.
The contest was one to forget for his fellow paceman Thakur, however, who bowled 10 balls on the opening morning before pulling up injured. "Very heartening to see the way Rishabh and Ajinkya have approached the innings because both have been patient and very disciplined", India's batting coach Sanjay Bangar told reporters.
The second Test between India and West Indies is being telecast on Star Sports 1 and 1 HD, Hindi 1 and Hindi 1 HD and Tamil 1.
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