Pant's meteoric rise in the rankings comes after his heroics in the recently-held COVID-delayed fifth Test between India and England in which he scored 146 and 57 across two innings.
India captain Rohit Sharma and his predecessor Virat Kohli remained static at eighth and 10th place respectively.
Ravindra Jadeja retained the top position among all-rounders, while Ravichandran Ashwin displaced West Indies' Jason Holder to be second.
Jadeja had risen to No.1 after his 175 not out and nine wickets in the first Test against Sri Lanka in Mohali earlier this month.
India's pace spearhead Jasprit Bumrah has jumped six spots to attain fourth ranking in the latest ICC Test Rankings for bowlers.
Ravindra Jadeja unbeaten 175 lifted him up to 17 places from 54th to 37th with the bat and he added nine wickets to move up to 17th with the ball.
The low scores and one-sided defeat have led to a fall in rankings for most India players with off-spinner Ravichandran Ashwin being the notable exception.
The 28-year-old's second Test double ton has taken his tally to 945 rating points, helping him share the second spot in the all-time list.
The four top-ranked Test teams: India, Pakistan, Australia and England are separated from each other only by 10 points.