England, set 500 to win, a target way in excess of the Test record fourth innings winning score of 418 for seven made by the West Indies against Australia in Antigua in 2003, finished on 369 for six.
Matt Prior was 12 not out and Ryan Sidebottom three not out while Kevin Pietersen top-scored with 101.
Rahul Dravid's men, ahead after a seven-wicket win at Trent Bridge followed a gutsy draw at Lord's, emulated the 1971 and 1986 teams by winning a series in England for only the third time in 15 tours dating back 75 years.
"It makes me feel proud to be captain of this team. Everyone has really contributed to the victory," said Dravid.
"It's a fitting tribute after so many years to go home with a victory. It's what we came here for and we deserve it. Hats off to the boys, they had a great series."
For England the draw meant the end of a six-year unbeaten run in home Test series, encompassing eight wins and three draws in 11 campaigns, since they lost the 2001 Ashes to Australia.
England captain Michael Vaughan said: "Full credit to India they really put us under pressure from the first session.
"I'm really proud of how the team fought to get the draw. India just pipped it in the end. But we have to take positives. Our team is relatively young and learning fast.
"We just have to go away now and analyse the mistakes we've made."
England, at tea, were 232 for three, needing an improbable further 268 for victory.
But the first ball with the new ball saw Paul Collingwood lbw for 40 to fast bowler Shanthakumaran Sreesanth.
South Africa-born Pietersen's drive through mid-wicket off Sreesanth saw him to a 155-ball century with his 18th four, his 10th hundred in 30 Tests.
But four balls later Pietersen's loose drive off the paceman was caught at first slip by Dinesh Karthik.
It looked as if England's last two specialist batsmen would bat out the day but Ian Bell, after a run-a-ball fifty, was lbw for 67 on the sweep to leg-spinner Anil Kumble, a thorn in his opponents' side throughout this match.
England now had to survive at least 28 balls with just four wickets standing but Sidebottom held firm.
Sreesanth had earlier dismissed England captain Michael Vaughan for 42.
Vaughan was caught behind by wicket-keeper Mahendra Singh Dhoni after flashing outside off-stump.
Pietersen, before tea, exchanged angry words with Kumble after the bowler believed the non-striker had impeded him as he tried to field.
"He's a fierce competitor," said Pietersen of Kumble. "I was ball-watching and I think I just got in his way."
Dravid added: "Anil can get quite wound up. There's no prouder man than when he walks on the field for India."
England resumed on Monday on 56 without loss. Andrew Strauss was 23 not out and fellow left-handed opener Alastair Cook 27 not out.
Left-arm quick Rudra Pratap Singh struck with his fourth ball when Strauss, without a Test hundred for over a year, edged to second slip on 32.
Kumble then removed Cook on 43, when a genuine glance was well caught low down by VVS Laxman at short backward square-leg.
India had all but ensured against defeat with a first innings 664 - their record Test total against England - which included Kumble's unbeaten 110, his maiden century in his 118 Tests.
Kumble then became Test cricket's third most successful bowler outright, overtaking retired Australia quick Glenn McGrath's mark of 563 wickets, when he had Monty Panesar lbw to end England's first innings on 345 all out.
Dravid, who opted not to enforce the follow-on, declared India's second innings on 180 for six.
England and India meet again in the first of seven one-day internationals, at the Rose Bowl, on August 21.