India were 117 for two in reply to England's first innings 221, a deficit of 104 runs, at lunch on the second day as they looked to level the four-match series at 1-1.
Dravid was 44 not out and Sachin Tendulkar, bidding to become the first batsman to score 100 international hundreds, 14 not out.
Earlier Dravid and Venkatsai Laxman (54) kept England at bay with a second-wicket stand of 93 after coming together at nought for one after India lost opener Abhinav Mukund to the first ball of their reply on Friday.
India resumed with Dravid, second behind Tendulkar in the all-time list of Test run-makers, seven not out and Laxman 13 not out.
The experienced duo took the attack to England's seamers with four boundaries in as many balls.
Laxman cover-drove James Anderson to the rope and Dravid, who scored a first innings century during England's 196-run first Test win at Lord's, clipped Stuart Broad legside.
Then Laxman, in a superb piece of timing, guided Broad behind point for four with no more than a defensive push.
England were convinced they had Laxman, on 27, caught behind off Anderson and asked for a referral after Asad Rauf rejected their raucous appeals. But the replay technology in use this series detected no edge umpire's decision was upheld.
England captain Andrew Strauss was unable to bowl Graeme Swann as the off-spinner was off the field with a hand injury suffered when batting Friday.
Meanwhile Laxman completed a 104-ball fifty when he cover-drove Tim Bresnan, in for the injured Chris Tremlett, for the 10th boundary of his innings.
But Laxman was undone soon afterwards by a lifting Bresnan delivery he could only fend to wicketkeeper Matt Prior to leave India 93 for two.
His exit brought in Tendulkar, who walked out to a standing ovation from all around the ground. Tendulkar, dismissed for 34 and 12 when hampered by a viral infection during England's at Lord's, got off the mark with a superb back-foot cover-driven four against occasional medium-pacer Jonathan Trott.
England will replace India at the top of the ICC's Test Championship table if they win this series 2-0 or better.
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