Day 1 round-up:
West Indies were at one stage looking good, reaching 106 for 2 at lunch, but Shami's afternoon burst deflated the visitors who were then bowled out for 234 shortly after tea.
The inexperienced new-ball attack of West Indies didn't trouble the Indian openers Shikhar Dhwan (21*) and Murali Vijay (16*), who safely reached 37 for no loss at stumps.
Rohit becomes the 14th Indian to score a Test century on debut as Indian lead gets close to 100 on Day 3 of the first Test at against WI at Eden Gardens.
Earlier, West Indies skipper, Darren Sammy won the toss and elected to bat on a track that looked ideal for batting, but apart from Marlon Samuels (65) none of the West Indies batsmen impressed. Debutant Shami finished with figures of 4 for 71