Dravid stands behind Australian skipper Ricky Ponting, who continues lead the pack and Kumble, who is at eighth spot, holds a 16 point lead over nearest rival Shane Bond of New Zealand in the bowlers' list.
India continues to be fourth, just two points behind third-placed England in the Championship table.
Meanwhile, Pakistan now boasts two batsmen in top five places of the Player Rankings following their drawn encounter with England at Lord's.
Captain Inzamam-ul Haq has climbed one place to third in the list after twin half-centuries and he has been joined in the top five by Mohammad Yousuf, who made 202, his second successive Test double hundred against England.
Yousuf is up two spots to fifth place and now has his best ever ranking and highest tally of rating points.
Completing a trio of Pakistan batsmen in the top 10 is Younis Khan, who missed the Lord's Test through injury. He lies seventh in the table. The only players Inzamam now trails in the rankings are his opposite numbers Ponting and Dravid.
England, by contrast, has just one batsman in the top 10, Kevin Pietersen at 10th, but below him, several of his team mates are making positive moves.
Andrew Strauss's ninth Test hundred has seen him rise two places to 12th, overtaking teammate Marcus Trescothick in the process, while Paul Collingwood's Test-best 186 has boosted him up to joint 34th position with Shahid Afridi.
The rankings for Test bowlers have seen no changes in the top 20 with England's Matthew Hoggard still the highest-placed player from either side.
The seamer remains in fifth spot, ahead of injured teammate Andrew Flintoff in sixth and Pakistan fast bowler Shoaib Akhtar, in seventh position.
Further down the list, leg-spinner Danish Kaneria is holding firm in 13th place while Stephen Harmison remains 17th.
Sri Lanka spinner Muttiah Muralitharan remains top of the Rankings ahead of South African Makhaya Ntini.
In the rankings for Test all-rounders, Jacques Kallis still leads from Flintoff. Pakistan's Abdul Razzaq has moved up to 11th place in that list, ahead of Afridi (12th).
LG ICC Test Championship:
Top-10 Teams: 1. Australia (130), 2. Pakistan (120), 3. England (113), 4. India (111), 5. Sri Lanka (99), 6. South Africa (98), 7. New Zealand (92), 8. West Indies (72), 9. Zimbabwe (28), 10. Bangladesh (2)
Top 10 Batsmen: 1.Ricky Ponting (Aus) 931, 2.Rahul Dravid (Ind) 882, 3. Inzamam-ul Haq (Pak) 846, 4.Jacques Kallis (SA) 832, 5. Mohammad Yousuf (Pak) 828, 6.Matthew Hayden (Aus) 808, 7.Younis Khan (Pak) 788, 8. Mike Hussey (Aus), 9.Brian Lara (WI) 732, 10.Kevin Pietersen (Eng) 724
Top 10 Bowlers: 1.Muttiah Muralitharan (SL) 901, 2.Makhaya Ntini (SA) 841, 3.Shane Warne (Aus) 813, 4.Glenn McGrath (Aus) 811, 5.Matthew Hoggard (Eng) 776, 6.Andrew Flintoff (Eng) 759, 7.Shoaib Akhtar (Pak) 743, 8.Anil Kumble (Ind) 736, 9. Shane Bond (NZ) 720, 10.Chaminda Vaas (SL) 700
Top five all-rounders: 1.Jacques Kallis (SA) 486, 2.Andrew Flintoff (Eng) 454, 3.Shaun Pollock (SA) 302, 4.Daniel Vettori (NZ) 290, 5.Chaminda Vaas (SL) 271