England completed their first series victory in India for 27 years as Jonathan Trott and Ian Bell both hit centuries on the final day in Nagpur.
India took just one wicket all day as debutant Joe Root added an unbeaten 20.
England finished 356 runs ahead on 352-4 when stumps were drawn early.
Their final-day dominance was fitting because, since being beaten by nine wickets in the first Test, England have outplayed their hosts in every department.
While recent Ashes victories will rank as some of England's finest displays in recent years, former captain Michael Vaughan put the accomplishment into context by describing winning a Test series in India as the hardest thing to do in cricket.
It is only the fourth time in history England have won there, and it is the first time since David Gower's tourists were triumphant in 1984-85.
England also inflicted India's first series loss on home soil since the legendary Australia team of Shane Warne, Glenn McGrath and Ricky Ponting won in 2004 - a series which became billed as "The Last Step To Greatness".
Cook's team may not be "great" yet, but they certainly gave players like Sachin Tendulkar, Virender Sehwag and Mahendra Dhoni plenty to think about with their dominant performances.
Graeme Swann and Monty Panesar outbowled India's spinners, James Anderson underlined his status as one of the best seamers in the world, while - led by the insatiable run-scoring feats of captain Cook - all of England's batsmen scored runs.
Trott and Bell were the two players most in need of a good score on the final day of the match - and both delivered emphatically.
The Warwickshire pair posted their highest Test scores of the year, with a century particularly welcome for Bell who averaged just 18 in India before he came to the crease when England were stuttering slightly at 94-3 on the fourth day.
Scoring may have been slow, with Trott facing 310 balls and Bell 306, but it is a measure of England's progress that they suffered so few alarms on the final day after such a chastening start to the year.
Both Trott and Bell were part of the side in January which was bowled out for 72 against Pakistan, on their way to a series whitewash in the United Arab Emirates.
But there was no way Trott was going to allow the year to end on a sour note. He continued in a defiant manner on the fifth morning - timing the ball to perfection - as he eased a four through the leg side to bring up his eighth Test century.
It appeared he might bat throughout the final day until his dismissal just before tea. The 31-year-old chased a Ravichandran Ashwin delivery and chipped the ball into the hands of Virat Kohli at leg-slip.
Bell batted similarly serenely, but did enjoy a let-off on 75 when he slashed hard outside off stump and was dropped at slip by Sehwag.
He capitalised on his fortune late in the day when he completed his 17th Test century - the slowest of his international career - as he and Root, who swept Ashwin for six to compound the off-spinner's misery, closed out the historic and memorable series victory.
England, who consolidated their second-placed position behind South Africa in the ICC Test rankings, travel to New Zealand for a three-Test series in March before hosting the Kiwis in the summer ahead of back-to-back Ashes contests.