Kumble achieved the feat here at the Feroz Shah Kotla, when he went out for toss against Australia in the third Test of the Border-Gavaskar Trophy.
World's third most successful bowler, Kumble, who is currently playing his 132nd Test, went passed Kapil Dev and West Indies' Brian Lara, both of whom have played 131 matches and stands at joint sixth place along side former West Indies' captain Courney Walsh in terms of number of Tests played.
The 38-year-old Kumble is now behind England's Alec Stewart (133), Australian Shane Warne (145), India's Sachin Tendulkar, former Aussie captain Alan Border (156).
Former Aussie captain Steve Waugh heads the list with 168 Tests.
Kumble could have surpassed Kapil Dev's record in the second Test at Mohali but a shoulder injury forced the Indian captain to sit out of the match.
In the last match of the series in Nagpur to be played on November 6, Kumble will have an opportunity to move up in the list leaving Walsh behind and will draw level with Alec Stewart.