Published: 2017-08-06 21:59:12 BdST
The all-rounder claimed his ninth five-wicket haul as Sri Lanka, forced to follow on after being shot out for 183 in the first innings, made 386 in the second before collapsing minutes before the tea break on the penultimate day.
It was a first victory by an innings or more for India in Sri Lanka and, following their biggest victory by runs in Galle last week, ensured an eighth straight series triumph under Virat Kohli.
"We said this morning that even if we don't get wickets early on, we are going to enjoy the tough times because they really improve you as a side and you need those tough times to improve as cricketers," the India captain said.
"We were very happy that we went through that difficult phase as well, for you never want to get complacent as a side."
Kohli will fancy equalling Australia's modern era record of nine consecutive Test series wins when India host Sri Lanka for three matches later this year.
Sri Lanka will take a modicom of confidence into that series from a second innings resurgence that was built around the 191-run stand between Dimuth Karunaratne and Kusal Mendis, who fell for 110 on Saturday.
Lefthander Karunaratne's gallant 141 merely delayed the inevitable on Sunday, though, as Jadeja (5-152) and spin partner Ravichandran Ashwin (2-132) tormented Sri Lanka on a worn-out track where the ball spun alarmingly and often kicked off.
Sri Lanka had resumed the fourth day on 209-2 at the Sinhalese Sports Cricket Ground with Karunaratne continuing his grim battle with the Indian bowlers.
Nightwatchman Malinda Pushpakumara threw away his wicket, attempting a bizarre reverse slog against Jadeja who dismissed Sri Lanka skipper Dinesh Chandimal for two in his next over.
Karunaratne and former captain Angelo Mathews resisted India for a while during a 69-run stand but Jadeja returned to wreck Sri Lanka after the lunch break.
Karunaratne's defiant knock, which included 16 boundaries, came to a cruel end when he was presented with an unplayable delivery that reared up, hit his gloves and ballooned into the air for Ajinkya Rahane to catch behind the wicketkeeper.
Mathews followed next, edging Jadeja to perish caught behind for 36 and Hardik Pandya claimed a couple of late wickets to hasten Sri Lanka's collapse.
"We were outplayed in the first innings both with bat and ball," Chandimal said after his team lost a Test inside four days for the second time in the series.
"Credit goes to them, they batted brilliantly in the first innings and put us under huge pressure. I'm really happy the way guys played in the second innings."
Jadeja, who smashed 70 not out and claimed seven wickets from the Test, was adjudged man-of-the-match.
Rahane was the bright exception in India's otherwise poor catching display, grabbing four in Sri Lanka's second innings alone.
Wriddhiman Saha also shone behind the stumps, taking a couple of spectacular catches, effecting a stumping and conceding only four byes on a pitch where the ball frequently misbehaved.
Pallekele hosts the dead rubber third and final Test from Saturday.