Put to bat first, India made 87 for three wickets in the pre-lunch session on a sunny day, with clouds hovering.
Rahane at 17 and Rohit Sharma at 9 were at the crease when lunch was called after the two-hour session, with 23 overs bowled.
India got off to a poor start losing opener Shikhar Dhawan (1) cheaply while skipper Virat Kohli (3) also perished soon after in the first hour of the day.
Tottering at 19/2, opener Lokesh Rahul (50) showed some resistance with a fine half century as he put on 58 runs for the third wicket with Rahane before all-rounder Roston Chase packed him back to reduce the visitors to 77/3.
Windies pacers Shannon Gabriel, debutant Alzarri Joseph and Chase shared the three wickets each.
The 24-year-old Rahul continued with his brilliant form from the second Test at Kingston in Jamaica where he scored 158 in 303 balls, with 15 boundaries and three sixes.
The Bengaluru lad, however, got caught in the short fine leg by Kraigg Brathwaite in the 20th over to a raising ball of Chase just after scoring his seventh half-century in Tests in 65 balls, with six boundaries.
For the hosts, Joseph bagged his first Test wicket when Darren Bravo caught the Indian captain at first slip in his second over and sixth of the innings.
Earlier, Gabriel packed off opener Dhawan in the third over, caught behind by wicketkeeper Shane Dowrich.
Both the teams have made changes after the draw in the second Test with India retaining Rahul in place of a fit-again Murali Vijay. Sharma was brought in place of Cheteshwar Puja, while all-rounder Ravindra Jadea and pacer Bhuvneshwar Kumar were included, replacing leg-spinner Amit Mishra and pacer Umesh Yadav.
For the hosts, opener Leon Johnson and pacer Joseph made it to the playing XI replacing Rajendra Chandrika and leggie Devendra Bishoo.
India are 1-0 in the series after winning the first Test at Antigua.
Brief Scores: India 87/3 (Lokesh Rahul 50, Ajinkya Rahane 17 not out, Shannon Gabriel 1/27, Roston Chase 1/16)
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