Kumar (3-34) bowled an incisive spell on either side of lunch to leave the hosts' top-order reeling after India had been bowled out for 295 runs in their first innings. England currently trail by 170 runs.
Gary Ballance (51*, 117 balls, 6 fours) and Moeen Ali (6*, 25 balls, 1 four) were at the crease, while India were unlucky not to have removed the former.
In the 40th over of the innings, bowled by Stuart Binny (0-24), he was given a life by skipper MS Dhoni as he failed to grab an edge that went between him and Shikhar Dhawan at first slip. The batsman was on 32 at that time and went on to get his half-century in the 52nd over of the innings.
India vs England Live Scorecard:
This was after Kumar had broken his lunch-stand with Ian Bell (16 runs, 56 balls, 2 fours) in the second session. They had added 20 runs in the morning and could only score 19 more before a short delivery surprised Bell and the ball kissed his gloves on its way to Ravindra Jadeja.
His dismissal brought first-Test centurion Joe Root to the crease and India were obviously desperate to see his back.
Ishant Sharma (0-21) and Mohammad Shami (0-25) were deployed then but they didn't get as much movement as Kumar. But to their credit they bowled well on an easing wicket and never let the pressure lift off.
Finally Jadeja (1-9) was introduced into the attack and he got the breakthrough needed. Root (13 runs, 50 balls) was adjudged LBW, albeit a big inside-edge which Australian umpire Bruce Oxenford failed to notice. Murali Vijay (0-2) bowled one over before tea as well.
In the morning session, Kumar removed Alastair Cook (10) first, caught behind by a diving Dhoni, as the English skipper's horrible run with the bat continued. It was brilliant bowling from the Indian medium pacer who set up Cook beautifully in the previous over and then snapped him up with a huge out-swinger off the first ball of the 11th over.
He then struck a second blow four overs later with opener Sam Robson (17) playing a loose stroke outside off-stump and was safely pouched by Dhoni as well.