Resuming their first innings on 308-4, the hosts quickly overtook the West Indies total but Holder and Shannon Gabriel were troubling the overnight batsmen.
Paceman Holder first surprised Ajinkya Rahane with extra bounce and two balls later trapped a scoreless Ravindra Jadeja lbw, dismissing the all-rounder who had scored an unbeaten century in India's comprehensive series opening win in Rajkot.
Rahane (80) featured in a 152-run stand with Pant, who could not reach triple figure either thanks to a brilliant catch by Shimron Hetmyer.
Pant attempted to punch a Gabriel delivery through cover but Hetmyer threw himself to pluck the spectacular catch. Pant's second successive innings of 92 contained 11 boundaries and two sixes.
Ravichandran Ashwin contributed a handy 35 down the order before becoming Gabriel's third victim.
Shardul Thakur, who bowled only 10 deliveries in his test debut before leaving the ground with a groin injury on Friday, returned to bat and was unbeaten on four.
(Reporting by Amlan Chakraborty in New Delhi; editing by Peter Rutherford)
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