The Indian off-spinner, who now has 372 rating points in his kitty, has displaced South Africaâ€™s Vernon Philander (365) at the top of the ICC Player Rankings for Test all-rounders.
Bangladeshâ€™s Shakib Al Hasan was at third spot while Englishman Stuart Broad has moved ahead of Australiaâ€™s Mitchell Johnson in fourth position.
Meanwhile, Sri Lankaâ€™s Kumar Sangakkara has regained the number one Test batsman spot following his 10th double century in Galle against Pakistan while Indiaâ€™s Cheteshwar Pujara and Virat Kohli slipped down the ladder.
Sangakkara, who won the ICC Cricketer of the Year and ICC Test Cricketer of the Year awards in Colombo in 2012, scored 221 and 21 in the Test, which earned him 31 ratings points that helped him dethrone AB de Villiers from the top pedestal.
The South African had snatched the number one spot from his team-mate Hashim Amla in October 2013 and spent a total stretch of 287 days and 33 Tests at the top.
Sangakkara had first surged to the top of the batting charts in December 2007 when he replaced Ricky Ponting, while he last claimed the top spot in November 2012 in Galle before Australiaâ€™s Michael Clarke dislodged him following his 230 against South Africa in the Adelaide Test.
Sangakkara has now spent a total of 81 Tests and 671 days as the top-ranked Test batsman. ICC Hall of Famer Garry Sobers holds the record for the most Tests spent as number one with 189, while Viv Richards is second with 179.
Mahela Jayawardena, playing his last Test series, has retained 14th position following his contributions of 59 and 26, but will seek to make his farewell Test a memorable one, which can potentially help him end higher on the rankings table.
Pujara lost two spots to occupy 12th spot though he remained the highest-ranking Indian while another struggling team-mate Kohli slipped five places to 20th.
In the Reliance ICC Player Rankings for Test bowlers, Englandâ€™s win against India at Old Trafford by an innings and 54 runs has seen its bowlers charge up the rankings table.
James Anderson has climbed two places to grab fifth spot following his three for 46 and two for 18, while man of the match Stuart Broad has propelled four places to ninth spot following his figures of six for 25 in Indiaâ€™s first innings.
Broadâ€™s movement now means England has two bowlers inside the top 10.
Moeen Aliâ€™s four for 39 in Indiaâ€™s second innings has allowed him to jump four places to a career high 33rd spot.
Ashwin remained the highest-ranking Indian bowler though he lost one spot to be at 13th while Pragyan Ojha and Ishant Sharma are at 15th and 20th respectively.