A draw or an Indian win, which would have sealed a series victory for the home side after their earlier win in Mohali, would have catapulted Rahul Dravid's side ahead of the tourists.
But England's success, their first Test win in India for 21 years, means the series ended 1-1 and has ensured they remain the nearest challengers to runaway leaders Australia.
England have 113 rating points in the Test Championship table, 16 points behind Ricky Pontings team, while India are a further two rating points back on 111.
India did hold second spot in the table for just over a month from mid-December when they overtook England, thanks to a combination of their own 2-0 series win against Sri Lanka and Englands 2-0 loss in Pakistan.
But their 1-0 series loss to Pakistan earlier this year dropped them back down the table to third and the defeat in Mumbai means they have missed the chance to regain the second spot.
An India win in Mumbai would have sealed a 2-0 series win and taken them to 115 rating points while dropping England to 110, while a draw would have given India a 1-0 success, lifted them to 114 and seen England slip to 111 rating points.
Indias next chance to gain rating points in the table is their four-Test series against the West Indies that starts in June. Ahead of that, Englands next Test action starts in May when they face Sri Lanka in a three-match series.
LG ICC Test Championship Team Rating: 1. Australia 129 2. England 113 3. India 111 4. Pakistan 108 5. New Zealand 100 6. South Africa 99 7. Sri Lanka 97 8. West Indies 73 9. Zimbabwe 27 10.