The hosts then trampled Sri Lanka 10-1 on the follow-on in their second innings at lunch on the third day in Mohali.
Facing a 400-run deficit in the first innings after India's 574-8, the tourists lost Lahiru Thirimanne to Ravichandran Ashwin's delivery as India clinched Virat Kohli's 100th Test win within three days. .
Jadeja scored a Test best 175 with the bat on Saturday and 5-41 with left-arm spin as Sri Lanka fell 161-4, losing their last six wickets for just 10 runs.
Pathum Nissenka topped with an unbeaten 61 as he and his overnight partner Charit Aslanka, resumed at 108-4, after an inspired spell of bowling led by Mohammed Shami and Jasprit Bumrah for nearly an hour at the start. Stand firmly in front. Of the day
After a successful review, Bumrah eventually broke with the wicket of Aslanka, trapping the left-hander lbw for 29.
Nissenka, who escaped early respite when Shreyas Iyer was dismissed for 26 off Ashwin, scored his fifth Test fifty in his seventh match and raised hopes of a comeback.
But Jadeja struck twice in an over to send back Niroshan Dickwella and Suranga Lakmal and expose the Sri Lankan tail.
Wickets kept falling and Jadeja scored two runs in two balls to complete the Sri Lankan reply in the first session.