Kohli extended the imperious form that saw him reign in all formats in 2016 to score his 27th ODI hundred and he was ably supported by Jadhav, 31 years old and playing his 13th ODI, during a partnership of exactly 200 that set up India to achieve their joint second-highest successful chase. Victory was completed with 11 balls to spare as Hardik Pandya followed up his two wickets with a cool-headed and inventive 40 not out to guide India home.
Kohli was visibly anguished to be dismissed with 88 still needed and Jadhav, struggling with cramp, fell shortly after to give England hope of pulling the match back. In the end, defending the short boundaries was too difficult a task, with only Jake Ball - who took 3 for 67 - and Chris Woakes going at fewer than India's required rate of seven an over.
Half-centuries of varying tempo from Jason Roy, Joe Root and Ben Stokes took England to what seemed a formidable total - the seventh time they had touched 350 since the 2015 World Cup - but, crucially, none of their early successes with the ball included Kohli. Stokes finally induced an error after Kohli and Jadhav had raised the double-century stand - India's second-highest for any wicket in ODIs - and Jadhav was then reduced to standing and swinging as cramp prevented him from running.
Stokes, with the fastest fifty by an Englishman against India, had provided the high-velocity finish England needed to set a challenging target. Their innings had threatened to subside after the dismissal of Root for 78 but Stokes hit the pedal in response, going from 14 off 19 to a 33-ball fifty in a starburst of sixes, as 105 runs flowed from the last eight overs to give England their highest ODI total in India - surpassing the 338 made in Bangalore at the 2011 World Cup (which also wasn't good enough for victory). Only twice had India chased as many, during their 2013-14 series with Australia.
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Kohli, in his first match since succeeding MS Dhoni as ODI captain, may have been frustrated with his bowlers at halfway but he set about making up for it himself. He wanted to bat second and showed his relish for the chase, cracking his fourth ball into the stands and taking every opportunity to put pressure on England as the bowlers sought wickets. Five sixes rained from his bat in all, along with numerous more subtle dissections.
Jadhav made an ODI century against Zimbabwe in 2015 but has had to bide his time with India, despite a List A average approaching 50. With Kohli looking as regal as ever, he just needed someone to stay with him, but Jadhav did more than that. He outscored Kohli during their partnership and was particularly severe on Adil Rashid, one of the stars of England's white-ball revival, who was twice hit out of the attack. At 262 for 4 with 14 overs to go, India were favourites and late strikes from Stokes and Ball could not derail them.
The outcome had been less certain after David Willey removed both openers, then India's veteran middle-order pairing of Yuvraj Singh and Dhoni also fell cheaply. Yuvraj, playing his first ODI in more than three years, sent his first scoring shot over the rope at deep midwicket, a throwback to his days of youthful marauding, but was caught tamely down the leg side off Stokes; Dhoni departed in the next over, top-edging a misbegotten pull to midwicket off Ball to leave India in trouble.
This England one-day side have come to India as both a curiosity and a threat. Their pumped-up approach has made them the fastest-scoring side in ODIs since a dismal showing at the last World Cup and subject of genuine interest in a country that knows more about limited-overs success than most - and one where England have tended to fail in coloured clothing. Eoin Morgan's side have got into the habit of breaking records and you can now throw in the highest ODI total England have failed to defend.
Some of that spark was provided by England's daring run to the final of last year's World T20 in India. Roy was one of the breakout stars of that tournament and he continued to show a liking for the conditions after Kohli chose to insert England. Roy played several crisp drive and flicks, either side of overturning an lbw decision after being given out on 18, to give the innings its early impetus.
His endeavour allowed Alex Hales to settle in, as is his preferred method, but the partnership was broken on 39 when Jasprit Bumrah's flat throw from deep-backward square leg caught Hales millimetres short. Roy's blade continued to flash, the pick of his fours a beautifully timed straight drive off Bumrah, during a 36-ball half-century as England ended the opening Powerplay on 67 for 1 (Roy with 52 of them). Then came the challenge of spin.
Root took his time to adjust and was mostly content to deal in dabs and deflections, although he did clear the ropes with a lofted sweep off Jadeja after reaching his fifty, from 72 balls. England played the spinners intelligently, with only Ravindra Jadeja taking a wicket, although Roy had a life on 66 when top-edging a reverse-swipe off R Ashwin to short third man, where Umesh Yadav couldn't hold on. He was finally removed in the following over, walking past a non-turning delivery from Jadeja to be stumped.
Morgan, back to lead England after opting out of the tour to Bangladesh, came into his first ODI since England lost to Pakistan at Cardiff in September having made scores of 3 and 0 in the warm-ups. After watchfully accruing four off 12 balls, he struck the first six of the innings, slog-sweeping over midwicket as Ashwin's spell turned expensive, but just when he appeared set for some steady middle-overs accumulation a thin edge behind - undetected by the umpire but confirmed by DRS - ended his stay