Meanwhile, India won the series 2-0 as Umesh Yadav's 10 wickets in the match starred in the victory.
Left with a paltry target of 72, India romped to victory late in the day, with openers Prithvi Shaw and Lokesh Rahul both stroking 33 not out, to keep West Indies without a Test win on Indian soil in 24 years.
Pant was batting on 85 at stumps with Rahane on 75 with India, who won the first test in Rajkot inside three days, almost wiping out the deficit.
Pacer and skipper Jason Holder returned with impressive figures of 5/56 as he shattered the Indian lower middle order.
Rahane's overnight partner Rishabh Pant was also denied a century when he was caught on 92 by Shimron Hetmyer in the covers off fast bowler Shannon Gabriel, who ended with three wickets.
Fast bowler Shannon Gabriel claimed three for 107, while left-arm spinner Jomel Warrican, in his first Test in almost three years, ended with two for 84.
Kuldeep Yadav too fell cheaply to Holder after contributing six runs while Umesh Yadav (2) also failed to make much impact as India's scorecard read 339/9.
His maiden century on debut came against West Indies in the first Test, whereas he followed that up with knocks of 70 and 33 not out in the second Test, thereby being adjudged Man of the Series.
The 18 years old Prithvi Shaw, who made his first worldwide century on his Test debut is likely to open with Rohit Sharma during the ODI series against Windies starting from October 21.