The 29-year-old Kohli had a total of 912 points, 17 points behind Australia's Steve Smith, who is comfortably placed at the top of the Test player ranking. Pujara, on the other hand, had 810 points.
India Test spinner Ravichandran Ashwin slipped one place in the bowlers ranking to take the fifth position with 803 points, while Ravindra Jadeja held on to his second spot in the all-rounders ranking.
South Africa opener Aiden Markram, meanwhile, sustained his surge towards the top during an amazing first year in Test cricket, making his way to ninth position among the batsmen ranking, which also took into account performances in the drawn second Test between New Zealand and England in Christchurch.
The 23-year-old's knocks of 152 and 37 not only contributed to South Africa's massive 492-run victory over Australia in Johannesburg for a 3-1 series win but also helped him move up six places to ninth position.
Markram has broken into the top 10 for the first time and is now among a select group of 10 cricketers led by Don Bradman who have scored 1,000 runs or more in their first 10 Tests.
Markram's opening partner Dean Elgar, too, has advanced after scoring 100 runs in the Test, including a knock of 81 in the second innings, while captain Faf du Plessis (up five places to 17th) and Temba Bavuma (up 12 places to 39th) are the other South Africa batsmen to make significant gains.
For Australia, captain Tim Paine has jumped eight places to 53rd position while for England, captain Joe Root moved up one place to third. Wicketkeeper Jonny Bairstow was up by three places to 13th and Mark Stoneman moved 14 places to 64th.
Among bowlers, South Africa pacers made gains after ruling the roost in Johannesburg Test.
Pace bowler Vernon Philander's player of the match effort of nine for 51 has lifted him six places to third and player of the series, Kagiso Rabada, remains at the top, adding three points to take his tally to 902.
Morne Morkel, who first broke into the top 10 in January 2010, touched 800 rating points for the first time in his career and is now ranked joint-sixth along with Australia's Pat Cummins, who has risen up from 18th with nine wickets in Johannesburg.
In other movements, New Zealand's player of the match Tim Southee has moved up three places to take the 13th slot, while Stuart Broad has gained five slots to reach 12th place.
Meanwhile, New Zealand have leapfrogged Australia to third place in the ICC Test Team Rankings.
The swapping of places has resulted in a clear gain of USD 100,000 for New Zealand as they will now receive USD 200,000 from ICC for taking third spot at the cut-off date of 3 April.
Australia will get half that amount after finishing fourth.