Chasing a stiff target of 326, India lacked the batting firepower on a placid track and were restricted to a 316 for 9 in a high-scoring contest to concede a 1-0 lead to visitors in the five-match series.
Opting to bat first, England rode on a record 158-run opening stand between captain Alastair Cook [ Images ] (75) and in-form Ian Bell [ Images ] (85) to post an imposing 325 for 4 at the newly built Saurashtra Cricket Association stadium.
The Indians conceded as many as 38 runs in the final two overs, with Ishant Sharma [ Images ] and Bhuvneshwar Kumar giving away 20 and 18 runs respectively.
The late flourish by England proved costly for the hosts in the end.
India began the run chase in right earnest, with Ajinkya Rahane [ Images ] (47) and an out-of form Gautam Gambhir [ Images ] (52) adding 96 runs for the opening stand, but both were guilty of frittering away a good start.
Yuvraj Singh [ Images ] (61), Suresh Raina [ Images ] (50) and skipper Mahendra Singh Dhoni [ Images ] (32) were other notable scorers, but, again, none of them could translate the start into a match-winning effort.
Off-spinner James Tredwell was the pick of the English bowlers, scalping four for 44, while Jade Dernbach chipped in with two wickets.
It was a creditable turnaround for the visitors, who came into match with back-to-back defeats in the warm-up games against India 'A' and Delhi [ Images ] respectively.
The victory is England's 14th in 41 ties between the two teams in India.
The teams will now travel to Kochi for the second one-dayer on January 15.
The last two overs cost India 38 runs and with it the match in the final analysis.
India commenced the stiff run-chase, having earlier made a winning score of 325 for 5 against the West Indies [ Images ] in November, 2002 at Ahmedabad [ Images ] their highest at home -- on a very sound note.
Openers Gambhir and Rahane batted confidently against the pace bowlers to rattle up quick runs before both perished to off spinner Tredwell in successive overs.
Both batsmen played the flick, glance and slash well to gather runs at a fast clip and Gambhir even struck fast bowler Steven Finn for three successive fours in the latter's third over in which the English bowler conceded 17 runs.
The 50 was raised in the seventh over before there was a minor scare when Gambhir narrowly made it home after sprinting for a second run to deep square leg.
But the advent of double off-spin in the form of Tredwell and Joe Root brought down the run-rate a bit and in their eagerness to up the tempo both openers fell.
Rahane was the first to go when he failed to reach the pitch of the ball after stepping out to Tredwell and lofted a catch to long off to the 57th ball he faced.
Tredwell sent back Gambhir soon after the left-handed batsman had surged to his half century and the Indian 100 had come through a catch at short mid wicket when the batsman flicked the off-spinner.
From 96 for no loss, things became tougher for the hosts at 102 for 2 in the 19th over and at the end of the 20th India were 104 for 2, eight runs off their rivals' score at the same stage. By the halfway stage, the difference was nine in favour of England.
But Raina's departure in the 42nd over followed by the successive dismissals of skipper Dhoni and Ravindra Jadeja [ Images ] in the 45th over virtually sealed India's fate.
The rest of the batsmen were not up to the task of scoring the remaining runs though Ravichandran Ashwin (13) and Bhuvneshwar Kumar (20 not out) brought the hosts closer to the target with a partnership of 24 for the 8th wicket but the target proved just beyond reach.
Earlier, Cook, who had buried India with three centuries while totalling 562 runs in the four-Test series won by England last year, and Bell compiled a partnership of 152 for the first wicket, breaking a 30-year record for England against the hosts in the process.
Left-handed Cook scored 75 off 84 balls, inclusive of 11 fours and six, while his right-handed partner was slightly more aggressive in making 85 off 95 balls, inclusive of nine fours and a six.
Pietersen (44 off 45 balls) and Morgan (41 off 38) put on a breezy third-wicket stand of 76 runs in 9.5 overs before both fell in 12 balls to Ashok Dinda [ Images ].
However, Samit Patel smashed 44 not out off 16 balls, inclusive of six fours and a six, and added 70 runs in the last six overs with Craig Kieswetter, who was unbeaten on 24 off 20 balls, inclusive of a four and two sixes.
Most of the Indian frontline bowlers were expensive. Ashok Dinda, who was preferred over Shami Ahmed despite the latter's impressive debut against Pakistan in Delhi last Sunday, was the most successful with two wickets for 53 runs.
Ravindra Jadeja (0 for 46 in 10 overs) and Suresh Raina (1 for 18 in 5 overs) bowled economically on a batsman-friendly wicket.
Ashwin was expensive, with figures of none for 61 in nine overs.
Senior placer Ishant Sharma conceded 86 runs in his 10 overs, including 20 in his last, his worst display in his 51 ODIs, while rookie Bhuvneshwar Kumar was also punished by the England batsmen.
Surprisingly, not a single over was given to known partnership-breaker Yuvraj Singh.
England, who had lost their previous ODI series in India 0-5 four years ago, set the hosts a stiff asking rate of 6.53 to win the game and take a 1-0 lead in the best-of-five rubber.
The Indian bowlers leaked runs aplenty in the face of the sustained assault on a good batting track by the England opening duo after Cook won the toss and chose to take first strike.
There were no false strokes from Cook and Bell barring an edged shot for four by the latter, that saw Dhoni and lone slip Ashwin looking at each other as the ball bisected the duo, off Bhuvneshwar Kumar.
Right-handed Bell was the more aggressive batsman initially. Cook hit his first boundary in the sixth over and struck two more in the same over of Ishant Sharma to banish the lanky right-hand pacer from the attack.
Bell was also rapped on the pads by Bhuvneshwar but umpire Steve Davis did not uphold the appeal. Thereafter, the opening pair did not give the Indians a chance till Bell was run-out by a superb piece of fielding by Ajinkya Rahane in the 28th over.
After 10 overs, the score was 54, and with the introduction of spin the run-rate dropped below five before it picked up again as the 100 came in the 19th over.
At the end of the 20th over, the score was 112 for no loss, the duo's second century stand for the first wicket in nine attempts.
Bell had earlier stepped out to left arm spinner and local boy Ravindra Jadeja to cart the bowler over the long-off region for the first six of the game and then reverse hit the spinner for another four to reach 50 in 60 balls.
Cook started to attack Ashwin and slog swept the off-spinner for a four and a near four which was stopped on the boundary line.
Ashwin, after a four-over first spell for 20 runs, changed ends but failed to stem the flow of runs, with Cook, who had scored plenty against him in the preceding Test series, once again exercising his dominance.
A four and a single off Ashwin helped Cook complete his 50 in 50 balls, with the help of nine fours.
In the next over England's captain carted the off-spinner for a six over long-off and a pulled four to spoil his second spell in which Ashwin gave away 22 runs in three overs.
The blows helped the partnership assume record proportions, overtaking the previous first wicket highest stand of 133 between Barry Wood and Chris Tavare in 1982 at Headingley.
It was the 82nd ODI meeting between the two countries.
Suresh Raina was brought on for Ashwin and in his second over came the much-needed breakthrough for the hosts when Bell was run-out at the striker's end through a smart pick-up and accurate throw at the stumps by Ajinkya Rahane, as Cook called him for a sharp single after inside edging to fine leg.
The partnership was snapped in the 28th over after the openers had laid a splendid platform for the others to take advantage of.
Then Raina struck another blow by inducing a top-edged sweep from Cook to send back the England skipper via a catch by Rahane at the same fine leg position, four overs later.
The loss of the two openers within a short span and for the addition of just 14 runs brought the home side back into the innings as at the start of the bowling power-play, England were 188 for 2 in 35 overs.
But Ashwin and Sharma were incapable of stopping the rampaging duo of Pietersen and left handed Morgan in this five-over period as 44 runs were scored by the visitors, who raced to 232 for 2 by the end of the 40th over.