Kumble, who is now the fifth bowler to claim 500 Test wickets, captured the wickets of opener Andrew Strauss (13), Ian Bell (57) and Paul Collingwood (14). His tally of wickets has now risen to 504 in 105th Test.
Harbhajan Singh and medium pacer Munaf Patel got one wicket each.
Munaf gave India the first breakthrough having opener Alasair Cook (2) caught by wicketkeeper Mahendra Singh Dhoni. England had only seven runs on the board then.
Harbhajan then removed dangerous Kevin Pietersen (4), who had contributed 64 runs in England's first innings total of 300 all out, caught by Dravid at first slip.
Dhoni was outstanding behind the wickets as he accepted three sharp catches while, Dravid, positioned at first slip, grabbed two catches.
Kumble was going great guns in England's second innings. He had left-handed opener Strauss out for a bat-and-pad decision given after it was referred to the third umpire.
Collingwood also fell in Kumble's trap. The ace leg-spinner first wasted a difficult chance to accept a return catch after running a few yards. However, he got him caught by Dravid in the slip in the same over for 14.
With the departure of Collingwood, the visitors were virtually fighting with their back to the wall as they were four down with the scorecard reading just 88.
Kumble then broke the backbone of England batting when he had the dangerous Ian Bell who completed his half century (57) with the help of seven fours from 137 balls.
Harbhajan was lucky to be awarded the wicket of Kevin Peitersen.
His delivery hit the forearm of Pietersen but was given out, caught by Dravid at first slip.
Earlier, Munaf Patel claimed his fourth wicket on debut after sending Alastair Cook (2), caught by Dhoni, to the pavilion.
The medium pacer from Gujarat had bagged three wickets in England's first innings.
At close of play on the penultimate day, captain Andrew Flintoff and wicketkeeper Geraint Jones were batting on 16 and one respectively.
With only one day left in the Test, England were just 74 runs ahead with five second innings wickets in hand. The Test is now poised for an interesting finish.
Earlier, the hosts' tail wagged as Kumble (32) and Harbhajan (36) made valuable contributions to consolidate the good work done by captain Rahul Dravid and Irfan Pathan and helped India take a handy 38-run first innings lead, scoring 338 all out in reply to England's 300. This was after Dravid made a cautious 95 and Pathan struck a quickfire 52 to carry India to safety from their overnight total of 149 for six to 269 for seven at lunch.
Dravid, who came at the fall of open Virender Sehwag's wicket at 18 yesterday, played the sheet anchor's role guiding India to safety before he returned to the pavillion five short of century.
He stayed at the wicket for 322 minutes and faced 208 deliveries slamming 10 fours, including two fine cover drives and one boundary at third man in one Andrew Flintoff over.
But the England captain got his revenge soon when he uprooted Dravid's middle stump by a ball which nipped back from off.
The Indian captain's sixth-wicket partnership with Pathan yielded valuable 76 runs which were compiled in 82 minutes and from 99 deliveries.
Dravid's dismissal silenced the crowd which was looking forward to a hundred from him.
Meanwhile, Pathan's hurricane 52 came from 58 deliveries after occupying the crease for 109 minutes. He slammed five fours and one six before he was caught by Paul Collingwood off the bowling of Flintoff.
Pathan drove off the front foot and Collingwood at backward point accepted the catch.
For the visitors, Flintoff was the most successful bowler as he claimed four wickets for 86 runs.