Bell recovered from a tentative start to exhibit trademark elegance, bringing up his first hundred in 26 innings by thumping Ravindra Jadeja down the ground for six before hitting the spinner for two more boundaries and another maximum in the same over.
England, 1-0 down in the five-match series after losing at Lord's last week, declared on 569 for seven in their first innings after a quickfire 85 full of expansive strokes by new test wicketkeeper Buttler.
Struggling India then closed on 25-1 in their first innings, James Anderson snaffling Shikhar Dhawan (6) yet again with Alastair Cook taking the catch.
Previously beleaguered England, who have not won in 10 tests, will look to ram home their advantage on day three and try to avoid having to bat again if they can enforce a follow on.
"I feel like I've been playing well recently but I have found strange ways to get out so it's nice to get a big hundred and contribute," Bell told reporters.
"It's been frustrating for me personally and the team lately but hopefully we can push this game on and getting runs is a good habit to start."
Sunday centurion Gary Ballance, who shared a stand of 142 with Bell, was the victim of a poor decision just before lunch when he was given out caught behind for 156, despite no hint of an edge on replays.
After the interval, India captain Mahendra Singh Dhoni opted to utilise his seamers in one over spells, attempting to break England's concentration.
It paid dividends early on as Joe Root (3) got a regulation edge to Dhoni after being tempted into a prod outside off stump by Bhuvneshwar Kumar.
Clearly buoyed by taking his first wicket, Kumar added the scalp of Moeen Ali (12) by teasing the batsman into taking on the short ball which he bottom edged to Ajinkya Rahane at second slip.
Towards the end of the middle session, the ball began to nibble around in the overcast conditions and Buttler survived a third umpire review after Rahane thought he got his fingers to a low chance at second slip.
Buttler, replacing the injured and out-of-form Matt Prior, profited and demonstrated his prowess with an exhilarating stand of 106 with Bell.
"We know the potential he has from seeing him in the one-day game. He played with great instinct and he was outstanding," Bell said of Buttler.
"If we can get platforms he can come in and move us on to winning positions. He's an exciting player."
Bell's swashbuckling innings, which included 19 fours and three sixes, came to an end when he attempted to hit Kumar over mid-off but instead picked out Pankaj Singh.
Buttler played superbly in a situation conducive to his attacking one-day style, dispatching the bowling attack to all parts of the ground with ruthless power.
He survived a simple missed stumping by Dhoni and eventually played on to a Jadeja delivery as he sensed a debut ton, forcing a declaration from Cook.
"The wicket was quite easy for the batsmen and it has been a long time in the field for us," said Kumar, who took 3-101.
"We were expecting a response because after losing a test match you expect them to come back stronger but we tried our best to limit their runs."