The Indians have had a miserable summer having already lost the series as they trail 3-0, surrendering their world No 1 status to their opponents in the process, but they had looked as if they could put England in trouble when an impressive first session of bowling saw the hosts slip to 97 for two as both openers, Andrew Strauss (40) and Alastair Cook (34).
But Bell and Pietersen survived some testing bowling from the Indians initially, and made hay in the afternoon and evening sessions to see England to an imposing total of 456 for three at the close.
Pietersen was dismissed close to the end of the day on 175 as he was caught and bowled by Suresh Raina, but Bell will resume this morning with nightwatchman James Anderson on 181, 19 short of achieving his first Test double century.
England had started the day on the backfoot with Cook dismissed in the first over of the day, caught at slip by Virender Sehwag off Ishant Sharma without adding to his overnight score.
Strauss, the England captain, was soon back in the dressing room, too, nicking a delivery from Sreesanth to MS Dhoni, the Indian wicketkeeper and captain.
But Bell and Pietersen plundered the Indian bowling after that with an array of attacking shots and they put on 350 for the third wicket, the second highest in England's history, and keep their side's hopes of achieving a series whitewash alive.
Meanwhile, Cook is likely to lead an England team minus several star names in a one-day international (ODI) against Ireland in Dublin next Thursday.
The selectors are preparing to announce an unfamiliar line-up today for next week's one-off match against opponents who memorably beat England in their last meeting during this year's World Cup in Bangalore.
Captain Cook is not expected to be among a number of international regulars rested for the clash in Dublin, which is sandwiched between the Test series and five-match ODI series against India.
Instead, players on the periphery of the England team are set to be given a chance to impress in the encounter.
The squad for September's one-day series and Twenty20 international against India will be announced on August 27.