Shubman Gill stroked a fluent 75 not out from 135 balls, with 11 fours and a six, to steer India to 427/4 in 116 overs at lunch on Day 2.
Dhruv Jurel was unbeaten on seven at the other end.
India batted positively in the morning session, scoring 109 runs from 26 overs but West Indies managed to bag a couple of wickets.
Yashasvi Jasiwal stroked 175 before he was unfortunately run out after a huge mix up with his captain Gill.
Nitish Kumar Reddy promoted to No 5 failed to make it count, as despite being dropped on 20, he perished after scoring 43.
Gill helped India seize the momentum after Jaiswal's wicket at the start of the session, hitting boundaries regularly.
Jomel Warrican once again impressed as he got the wicket of Reddy, who holed out to long-on.
India will likely bat for another hour after the lunch break and declare after getting past 500.