India, at tea, were 149 for one, a first innings deficit of just 49 runs, with Karthik 77 not out.
Karthik with fellow opener Wasim Jaffer put on 147 for the first wicket to show there was more to India's batting than their much-vaunted middle-order.
India captain Rahul Dravid was unbeaten on nought.
At lunch, India were 40 without loss after Karthik (20 not out) and Jaffer (15 not out) had come through 16 testing new-ball overs.
Ryan Sidebottom saw his first delivery after the break steered off the back foot through point for four by Jaffer.
England captain Michael Vaughan brought on Paul Collingwood, no doubt hoping he could replicate the effort of India medium-pacer Sourav Ganguly who had opener Alastair Cook lbw on Friday.
Karthik, on 29, then saw a mistimed drive off Collingwood just about carry to James Anderson in the covers before lobbing him just short of mid-on.
Meanwhile fast bowler Chris Tremlett repeatedly beat the bat.
And when he did induce a false drive from Jaffer, on 32, Ian Bell dropped the difficult one-handed chance in the gully.
The introduction of Monty Panesar almost yielded a wicket first ball when Karthik, on 44, missed a sweep. But South African umpire Ian Howell rejected Panesar's vehement lbw appeal.
Jaffer, on 36, also survived a Panesar shout when it looked as if he might be 'hiding' his bat behind his front pad.
Karthik then completed his second Test fifty in as many innings with a trademark cover-driven four off Panesar, his eighth boundary in 95 balls.
The hundred partnership came up in the 32nd over.
It was the first century stand by an Indian opening pair in a Test in England since 1979 when Sunil Gavaskar and Chetan Chauhan shared a partnership of 213 at The Oval - India's all-time first wicket best against England.
Jaffer then completed his second fifty of the series, following his 58 at Lord's, off 101 balls with seven boundaries, before Kartik cover-drove Anderson for a couple of superb boundaries.
But the persevering Tremlett, with the first ball of his third spell, finally broke the stand when Jaffer was caught behind by Matt Prior off a steepling delivery for 62.
Tremlett, at tea, had fine figures of one for 18 in 11 overs.
Zaheer Khan, with a return of four for 59 in 21 overs, his best against England, and leg-spinner Anil Kumble (three for 32 in 12.3) needed fewer than 11 overs between them on Saturday to bowl out England.
The hosts had resumed on 169 for seven following Dravid's decision to field first in conditions helpful for swing bowling.
Brief Scores (at tea, D-2):
England Ist innings 198 all out (Cook 43, Ian Bell 31, Collingwood 28; Zaheer 4 for 59, Kumble 3 for 32) Vs India Ist innings 149 for 1 (Karthik 77 n o, Jaffer 62; Tremlett 1 for 18).