He has logged 336 points in a list headed by West Indian Jason Holder (407 points). Ashwin's spin bowling partner Ravindra Jadeja remained at second with 403 points, followed by Ben Stokes (397) of England and Shakib Al Hasan (352) of Bangladesh.
The 34-year-old Ashwin remained static at seventh among Test bowlers with 804 points while pacer Jasprit Bumrah, who was rested from the Chennai Test, also retained his eighth spot with 761 points with Australian pacer Pat Cummins (908) topping the chart.
Kohli, who made 0 and 62 in Chennai, retained the fifth position among batsmen with 838 points. Kane Williamson (919) of New Zealand retained the top position with Steve Smith (891) of Australia in second spot.
Another Australian Marnus Labuschagne (878) moved up to third while England captain Joe Root (869) slipped to fourth after his two innings of 6 and 33 in the Chennai Test.
Another Indian Cheteshwar Pujara -- 21 and 7 in Chennai -- slipped to eighth place with 727 points.