With just one wicket in hand and still trailing by 71 runs, India finished the day at 322 for nine in reply to England's first innings score of 393.
At the draw of stumps, Harbhajan Singh was yet to open his account.
Kaif and Kumble joined hands for India in the afternoon session with the home team looking down the barrel at 190 for seven. The two equalled the previous best Indian eighth-wicket partnership of 128 against England which stood in the name of Ravi Shastri and Syed Kirmani in 1981 in Delhi.
However, the two played sensible cricket and made most of the opportunities the visitors offered with both of them being given one life each.
Kumble got off the mark with a streaky four off Hoggard and in the next over Flintoff dropped a difficult return catch from Kaif when the batsman was on 18 in the team score of 194 for 7.
Kaif made the Englishmen pay for this lapse from their captain as he first defended stoutly and then grew in confidence as the moisture in the wicket evaporated with the sun beating down after the overnight unseasonal rains to play his trademark flicks and drives to telling effect.
The Uttar Pradesh batsman, who was playing for his place in the team, cover drove Steve Harmison, the biggest disappointment of the English bowlers today, to bring up the team's 200. He then slashed Harmison in the same over for a boundary over the slip cordon. Kumble at the other end was then given a reprieve when wicket-keeper G Jones floored a catch off the bowling of Harmison when the batsman was on 9 in the team total of 217 for seven.
While Kaif was the rock on which the Indian innings was built up, Anil Kumble mixed caution with aggression, not failing to score of any loose delivery. The two late cuts he played off left arm spinner Monty Panesar would have done any top order batsman proud.
Kaif in the meantime reached his 50 after he attacked Flintoff with the second new ball flicking him to the mid-wicket fence and then turning his attention to left-arm spinner Ian Blackwell on-driving and cover driving him for two boundaries. He reached his third Test fifty which came in 140 balls with five hits to the boundary.
Kumble then joined Kaif in completing his 50 with a couple to midwicket off Flintoff. Kumble's half century was studded with nine boundaries playing 133 balls.
Just when it seemed that the two would see the day through, Kumble tried to run a ball from Steve Harmison down to third man, but only managed to give a simple slip catch to Alastair Cook. Kumble made 58 with 10 boundaries facing 168 balls. India were then 318 for eight.