The 28-year-old Kohli scored 62 and six not out in the recently-concluded third Test to move to 833 points.
Top-ranked in Twenty20 Internationals and second in One-Day Internationals, Kohli will look to improve his ranking further in the remaining two Test matches against England.
Another Indian batsman to figure in top-10 was Cheteshwar Pujara, who occupies the eighth spot in the table, headed by Australia captain Steve Smith.
England's Joe Root is at the second position, having 14 points more than Kohli.
Ashwin has consolidated his position at the top in the Test all-rounders' rankings with 493 points, a tally not reached by anyone since retired South Africa player Jacques Kallis in 2008.
Ashwin's spin partner Ravindra Jadeja is the other Indian to feature in the top-10 of both Test bowlers' and all-rounders' rankings.
While he is holding the seventh position in the bowlers' list, Jadeja has gained two slots to reach a career-best fourth as an all-rounders after scoring a crucial 90 in his only innings in Mohali.
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