A 129-run opening stand between Craig Kieswetter (63) and skipper Alastair Cook (60) gave England the perfect platform to chase down a 272-run victory target but Jadeja took four for 33 as the tourists collapsed to 176 all out in just 37 overs.
Off-spinner Ravichandran Ashwin claimed three for 28 and part-timers Suresh Raina and Manoj Tiwary one wicket each for India, who failed to beat England in any form of the game on their recent tour.
India, put into bat, raced to 80 for nought. But they then slumped to 123 for four before captain Mahendra Singh Dhoni provided a late flourish with a sparkling unbeaten 75 off 69 balls to shepherd them to a commanding 271 for eight.
"It was a very ugly looking wicket and any ball could swing or keep low," Dhoni told reporters. "It was very difficult to score on so we were fortunate to score 271 -- 240 or 245 was in our mind.
"I wanted to stay to the end of the innings. It's important to see which bowlers are left and who you can target -- after that it's about who can bear the pressure well."
England looked very much in the run chase as long as Kieswetter and Cook were in the middle, the pair hitting boundaries at regular intervals.
Dhoni introduced spin in the eighth over but the breakthrough remained elusive until the 21st over when Varun Aaron bowled Cook to end his 61-ball knock.
Apart from the openers, only two England batsmen reached double figures against the Indian spinners who claimed nine of the 10 wickets.
"It's a bit of a shock, we were in control," said Cook. "We know you can lose clusters of wickets on the sub-continent but we didn't think you could lose all 10.
"It was a massive collapse. We haven't batted well enough ... we just got blown away."
Earlier, the left-right combination of Gautam Gambhir (38) and Ajinkya Rahane (42) gave India a solid start, adding 80 runs in 17 overs before Steven Finn triggered a top-order collapse with a double strike in the 18th over.
Finn induced Gambhir to drag his first ball of the over on to the stumps and pegged back scoreless Virat Kohli's off-stump with the last.
His new ball colleague Tim Bresnan removed Rahane in the next over as India slumped to 80 for three.
Suresh Raina was badly dropped by Graeme Swann in the slips to deny Finn his third wicket and he went on to make 38.
Raina celebrated the reprieve with two fours in that over and steadied the innings with Manoj Tiwary (24) but India still needed a late push to reach the 250-mark.
Fortunately for them, Dhoni, who has not been dismissed in his last six one-day innings, responded with an immaculately paced knock.
The right-hander began cautiously before stepping on the gas, milking the bulk of the 39 runs off the last two overs to power India to a total that proved beyond England's reach.
The teams play a lone Twenty20 International at the same venue on Saturday.
