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While Kohli moved up a place to career-best second in the batting table, Ashwin rose three places to a best-ever third position in the bowlers' list.
The latest rankings update, released a day after Sri Lanka beat India in the final of the tournament in Mirpur, reflects the performances in the semi-finals and final.
Kohli, named player of the tournament, ended as the highest run-getter of the tournament with 319 runs at an average of 106.33 and a strike-rate of 129.14. He scored an unbeaten 72 in the semi-final against South Africa and followed it up with a knock of 77 in the final against Sri Lanka.
These efforts helped Kohli gain 68 ratings points to move up to a best-ever 889 ratings points, just three behind number-one ranked Australia batsman Aaron Finch.
The only other India batsman in the top 10 is Suresh Raina, now in 10th place (down by three).
Sri Lanka's Kusal Perera, in fifth, is the only batsman from his side in the top 10.
South Africa captain Faf du Plessis has entered the top 10 for the first-time ever and is now in sixth place (up by 11). Close on his heels is teammate JP Duminy, in seventh place (up by one).
The other batsmen to move upwards outside the top 20 are Hashim Amla in 22nd place (up by two), Rohit Sharma in 26th (up by one), Dwayne Bravo in 29th (up by two), Angelo Mathews in 41st (up by six), Dwayne Smith in 47th (up by one), David Miller in 59th (up by two), Thisara Perera in 67th (up by three) and Ajinkya Rahane in 85th (up by four).
Meanwhile, India off-spinner Ashwin now shares the third position on the bowlers' table with Pakistan's Saeed Ajmal.
Ashwin finished with 11 wickets in the tournament at an average of 11.27 and an economy rate of 5.35 runs per over. Ashwin ended as the fourth highest wicket-taker in the tournament. He had spells of three for 22 in the semi-final against South Africa and one for 29 in the final against Sri Lanka. These efforts helped him gain 25 ratings points to end at a best-ever 711.
The bowlers' list is still headed by West Indies' Samuel Badree with teammate Sunil Narine in second place.