Kohli, who scored 169 and 54 in the first and second innings of the just-concluded third Test, is the best-placed Indian batsman in the list with 737 ranking points.
Cheteshwar Pujara and Murali Vijay are the next best Indian batsmen in the list at 19th and 20th spot after losing two and one place respectively. Ajinkya Rahane, who scored 147 and 48 in the third Test, also made a jump of 15 places to reach 26th spot.
Australia captain Steven Smith, who scored a Test best 192 in the first innings, has gained two places to claim fifth spot for the first time in his career. He now trails number-one ranked AB de Villiers, who has regained the top spot from Kumar Sangakkara.
Also moving in the right direction are Chris Rogers of Australia (24th, up by four places), Kraigg Brathwaite (37th, up by 11 places), Marlon Samuels (37th, up by seven places) and Dean Elgar (50th, up by 13 places).
In the ICC Player Rankings for Test Bowlers, Umesh Yadav and Mohammad Shami improved eight places each to be placed at the 36th and 38th spot in the list which is still headed by South Africa's Dale Steyn.
Australia's Ryan Harris has moved up two places to second following his six wickets at the Melbourne Cricket Ground (MCG), while Trent Boult has achieved a best-ever ranking of seventh after rising two places. Boult had figures of three for 25 and four for 100.
Bowler outside the top 20 and moving in the right direction include Neil Wagner (22nd, up by two places), Josh Hazlewood (53rd, up by 16 places) and Imran Tahir (58th, up by six places).
There is no change to the top five in the ICC Player Rankings for Test All-Rounders. Shakib Al Hasan of Bangladesh leads the field, followed by Vernon Philander of South Africa and India's Ravichandran Ashwin.

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