Kohli achieved a career-high 937 rating points after innings of 46 and 58 in the fourth Test.
The Indian captain, who has scored 544 runs in his eight innings this series, is 11th in the list of best ever in terms of rating points, just one adrift of a group of four - Gary Sobers, Clyde Walcott, Vivian Richards and Kumar Sangakkara.
Cheteshwar Pujara remains the second highest ranked India batsman in the list as he retained the sixth position. However, his unbeaten 132, which helped India take the first innings lead, lifted him from 763 to 798 points.
In the bowlers' list, pacer Shami progressed back to the top 20 after his six-wicket match haul lifted him three places to 19th position while fellow fast bowler Ishant Sharma's four wickets saw him move up one place to 25th position.
Jasprit Bumrah continued the strong start to his Test career, moving to a career-best 487 points while retaining 37th position after his fifth Test.
For England, all-rounder Sam Curran made quick gains while spinner Moeen Ali also moved up after the Southampton Test, which saw the home side winning by 60 runs on Sunday to take a winning 3-1 lead in the five-match series against India.
The 20-year-old Curran moved up 29 places to the 43rd position among batsmen after producing crucial knocks of 78 and 46 in the fourth Test match.
The left-hander, son of former Zimbabwe cricketer Kevin Curran and younger brother of England player Tom Curran, also gained 11 places to reach 55th place in the bowlers' list and 15th position among all-rounders after gaining 27 slots.
Player of the match Ali's haul of nine wickets helped him move up three places to 33rd position with a huge gain in rating points.
The off-spinner, who grabbed five for 63 and four for 71 in the two innings, has gained 66 points to reach 543 points in bowling, while also gaining one slot to reach seventh place among all-rounders.
Jos Buttler also gained 15 slots to reach a career-best 32nd position in the batsmen's list and 584 rating points, just five behind England all-rounder Ben Stokes, who has also gained three places to reach 29th position. While opener Keaton Jennings is another one to gain, moving up four places to 86th position in the list for batsmen.