The veteran Dravid (117) notched up his 34th century to equalled Sunil Gavaskar`s record but India lost six wickets for a mere 21 runs to allow the hosts come back into the game on a Trent Bridge track which provided assistance to quick bowlers.
Broad, who has been tormenting the Indians in the series, claimed the wickets of captain Mahendra Singh Dhoni (5), Harbhajan Singh (0) and Praveen Kumar (0) to record a hat-trick in front of his home crowd and change the complexion of the game at the fag end of the eventful second day.
Harbhajan`s LBW decision was though a howler from field umpire Marais Erasmus as the ball clearly got the edge from his bat before hitting the pads.
The visitors, trailing the four-match series 0-1, were comfortably placed at 267 for four at one stage before Broad`s career best 6/46 wrecked havoc to the Indian innings.
India could manage a first innings lead of just 67 runs though at one point of time they looked like taking a sizeable lead.
Dravid anchored the Indian innings brilliantly in difficult batting conditions while Yuvraj Singh (62) and VVS Laxamn (54) were the other notable contributors.
England were 24 for one at the close of play, still trailing by 43 runs with nine second innings wickets in hand.
Captain Andrew Strauss and Ian Bell were batting on six and nine respectively at the draw of stumps.