The 25-year-old from Chennai, who took five for 69 in New Zealand's second innings in the second Test at Bangalore, jumped seven places on the chart.
The off-spinner finished the two-match Test series with 18 wickets, and gained 26 places on the bowlers' table through the course of the series, as India defeated New Zealand 2-0.
Ashwin, who was named player of the series, also achieved a career-high rating of 591.
Ashwin's team-mate, Pragyan Ojha, ended with a match haul of seven for 148 and moved up a place to 14th, which is his career-best ranking. Ojha's overall rating of 675 is also his best-ever rating.
For New Zealand, fast bowler Tim Southee, who returned career-best figures of seven for 64 in India's first innings, has jumped 10 places to 40th. His overall rating of 432 is also his career-best to date, the ICC said in a statement.
India pace bowlers Zaheer Khan (15th) and Umesh Yadav (48th) slipped a place each.
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New Zealand bowlers, who dropped in the latest rankings are Doug Bracewell in 30th (down by one), James Franklin in 49th (down by five) and Trent Boult in 69th (down by six).
The rankings for Test bowlers is still headed by South Africa's Dale Steyn, with teammate Vernon Philander and Saeed Ajmal of Pakistan in second and third positions, respectively.
The two centurions in the Bangalore Test, New Zealand captain Ross Taylor and India's Virat Kohli, made upward movements in the batting chart. (MORE)