Kuldeep Yadav picked up 2-23, while Mohammed Siraj took 3-31 in 11 overs as West Indies were bowled out for 146 runs (45.1 overs) on Saturday.
The visitors had scored 162 runs in the first innings. In reply, India declared at 5-448 with a lead of 286 runs.
India had three centurions in their first innings — Lokesh Rahul (100), Dhruv Jurel (125) and Jadeja (104 not out).
"I have worked hard on my batting. I had been batting lower at eight or nine, but now I bat at number six. So there is no need to rush and I take my time," vice-captain and player of the match Jadeja said.
The second match in the two-Test series begins on October 10 in New Delhi.
West Indies had one good partnership to start the second session on day three. Justin Greaves and Alick Athanaze put on 46 off 87 balls for the sixth wicket.
Athanaze top-scored with 38 off 74 balls, with three fours. He was the first to go post lunch — a fine return catch by Washington Sundar (1-18).
West Indies slipped to 8-98 as Siraj trapped Greaves lbw for 25 and then had Jomel Warrican caught for a duck.
Jayden Seales delayed the inevitable with 22 off 12 balls, with two sixes, pushing the score past 100.
Jadeja and Yadav then wrapped up proceedings before the tea break, as India won without breaking a sweat.
Earlier, West Indies were 5-66 at lunch after India declared their first innings overnight.
Jadeja picked up 3-30 in the morning session to leave the tourists reeling in 27 overs by lunch.
West Indies' opening stand lasted only 7.2 overs before Siraj struck to dismiss Tagenarine Chanderpaul for eight. Nitish Reddy took a stunning catch at square leg to dismiss the opener.
Jadeja was brought into the attack early, and he dismissed John Campbell (14) and West Indies were 2-24. It shortly became 3-34 and 4-35 — Jadeja had Brandon King caught at slip for four and Yadav bowled skipper Roston Chase for one.
West Indies have not beaten India in 26 Tests — home or away — dating to 2002. They have lost four of the last five Tests in India by an innings' margin and lost the fifth by 10 wickets (2018).
It is the first time in 15 years that India have played a home Test without Virat Kohli, Rohit Sharma and Ravichandran Ashwin.
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