At the break, Jaffer on 43 and Dravid on 19 were at the crease and the hosts now need 305 runs for an unlikely victory in 60 overs, with nine wickets in hand.
Earlier, England declared their second innings at their overnight score of 297 for three and set a victory target of 368 for India in 90 overs.
India started disastrously as the swashbuckling opener Virender Sehwag fell without opening his account. It looked like Sehwag was in a hurry to finish off the match as soon as possible, as he went for the shots on each ball he faced.
Finally, he was dismissed in the fifth over, when he went for an expansive cover drive only to see the ball from first innings hero Matthew Hoggard sneak between the bat and pad and disturb his furniture behind the stumps.
Dravid then joined Jaffer and the two played carefully without taking any risks in the opening spell of Hoggard, who bowled accurately keeping the right length and placing the ball at right spot, thereby not giving any room for the batsmen to play shots.
Though Hoggard was not able to get as much swing today as he did on the third day's morning, he was extremely accurate and his first spell read 7-4-9-1.
At the other end, Steve Harmison also bowled well, but from one of his few loose balls Dravid got off the mark with a superb straight-drive.
Flintoff then brought himself on and Jaffer immediately showed how good he was on the leg side by flicking the England skipper to the square leg fence. In his next over, Jaffer followed it up with a terrific straight drive with the same result.
English brought in left-arm spinner Monty Panesar after 17 overs and Jaffer came into his own, driving Panesar for two glorious on-drives.
Both Dravid and Jaffer did not have any problem handling the England spinners, as Flintoff employed a double spin attack and brought Ian Blackwell from the Jaika End.