Sreesanth and Patel removed the English openers to have the visitors tottering at 31 for two in their second innings at close of play.
Owais Shah with 15 and night watchman Shaun Udal with two were at the crease as England extended their lead to 152 runs.
Munaf Patel struck the first blow for India removing first innings' centurion Andrew Strauss with Mahendra Singh Dhoni taking the catch behind the wicket for four runs.
Three overs later, Sreesanth removed the other opener - Ian Bell as he played away from his body for the edge to carry.
Dhoni. Bell made eight runs and England were 21 for two at that time.
Sreesanth could have had Udal also, but for the poor fielding of India, as Yuvraj Singh dropped the sitter at third slip.
Earlier, James Anderson, playing his first Test in a year, grabbed four important wickets, including that of the two main batsmen Sachin Tendulkar and Rahul Dravid and effected a brilliant run out of Dhoni, who top scored with 64, to put England in command in the 'must-win' Test for them.
Earlier, A superb counter attack of 55-run ninth wicket partnership between Anil Kumble and S Sreesanth helped India reduce the first innings lead, after the English pace trio had tightened its grip on this match. India were bowled out for 279 about 40 minutes before close of play in reply to England's first innings score of 400 to concede a first innings lead of 121.
India lead the three-match series following their nine-wicket win in the second Test at Mohali, while the first at Nagpur was drawn.
The hero of the day for England was swing bowler James Anderson, who was playing his first Test after a year's time, as he grabbed four wickets, two of them being of Sachin Tendulkar and Rahul Dravid, as well as Harbhajan Singh and Munaf Patel besides effecting a superb run out of Mahendra Singh Dhoni, who, with 64 was India's highest scorer to give England the advantage after the close of the third day's play.
Kumble and Sreesanth joined hands with India at 217 for eight and then proceeded to entertain the home crowd with some lusty hits, with Sreesanth being the more aggressive hitting Flintoff for two fours in an over and then Kumble smashing Matthew Hoggard over the slips for another boundary. The pair put on an invaluable 55 runs before Kumble was trapped leg before by Panesar for a well made 30.
India, resuming at 89 for three, needed their captain Rahul Dravid, playing his 100th Test and Yuvraj Singh to go on and stich a huge partnership to get back into the game. However, that was not to be as Yuvraj, in just the second over of the day, played a loose shot slashing at a delivery of Flintoff wide outside the off stump to be caught behind by Geraint Jones after adding just five runs to his overnight score of 32. India were then 94 for four and once again the onus fell on Rahul Dravid to bring India back into the game.
The England seamers, having tasted blood with the wicket of Yuvraj early, bowled with fire and purpose to push India further on the backfoot.
Flintoff and Hoggard bowled an inspired spell of fast bowling as they made the ball rear from a short of the good length and the former also hitting Dhoni on the back of his head.
The Indian wicket keeper, however, replied in the only way as he can pulling the England stand-in captain to the midwicket fence for a boundary and then following it up with a smashing cover drive.
Flintoff placed three fielders in the deep on the leg side in a bid to trap Dhoni but he did not fall prey and played sensibly.
Anderson was then brought on and he immediately had the Indians in trouble and but for the butter-fingered English fielders, he could have had more wickets to his name.
Dhoni was first given a let off when a powerful off drive went uppishly to Monty Panesar at mid-off but the spinner could not latch on to the catch to give the Indian wicket keeper a reprieve. Dhoni was then on 23 and the Indian score on 137 for four.