Opening batsmen KL Rahul (33 not out) and Prithvi Shaw (33 not out) then rattled off the required runs in just 16.1 overs to seal a second successive victory inside three days.
There was promise for the West Indies at one stage in the match after they bowled out India for 367 and limited the hosts' first innings lead to 56.
India dominated the last two sessions of the third day's play in the second and final Test match to crush West Indies by 10 wickets and complete a series whitewash easily on Sunday.
For India, it was their 10th series win at home since their last defeat against England way back in 2012. Sunil Ambris top-scored with 38, offering some resistance with skipper Jason Holder for the seventh-wicket, but the tourists were bowled out for just 127 in the final session. Earlier, Roston Chase completed his fourth test century before Umesh Yadav, who registered a career-best 6-88, dismissed him for 106.
Kieran Powell went to Ashwin and Hope's (28) attempts to steady the ship in a 39-run partnership with Hetmyer (17) were ended as the two men were removed in quick succession.
Post tea, West Indies were unable to salvage much from the second innings' wreckage.
Pant (92), who added seven more runs to his overnight score, got a short ball from Shannon Gabriel, which he pushed at only to be caught by Shimron Hetmeyer at cover point.
Towards the end, he played out a dramatic over to enable Shaw, India's teenage batting sensation, to hit the winning runs.
Without a score of note in his comeback series, Ambris tried to make his mark, carving out four fours off 95 balls in almost two hours at the crease.
With two runs added, at 70 for six, Shane Dowrich had his off-stump uprooted by Umesh off the inside edge for a first-ball duck, leaving the Windies tottering on 76 for six at the interval.