West Indies added only 16 runs to their overnight total but Roston Chase (106, 189 balls) however deservedly completed his fourth Test hundred before the innings wrapped up.
The Caribbeans could add only 16 runs in the morning session after Umesh Yadav polished off the tail with career-best figures of 6/88 in 26.4 overs.
On a reasonably good day, what stuck out like a sore thumb was yet another failure from opener KL Rahul (4). He has now 15 failures in 17 Test innings this year.
Young Prithvi Shaw lit up the morning, smashing his way to 70 off 53 balls to provide an initial momentum.
Skipper Virat Kohli (45, 78 balls) missed out on an opportunity to add another ton to his growing list of international hundreds as he looked in no trouble whatsoever during his stay at the crease.
But vice-captain Rahane slogged hard to remain undefeated on 75 off 174 balls.
Pant celebrated his ODI call-up with a second Test half-century, an attractive unbeaten 85 off 120 balls.
Together, the duo added 146 runs for the unbroken fifth wicket after India lost in-form skipper Virat Kohli (45) to be reduced to 163 for 4.
India are now only three runs short of West Indies' first innings total of 311.