India fast bowler Bumrah has achieved a career-high ranking of 33rd, after his three for 47 and three for 68 at Adelaide helped him to rise five places.
The 28-year-old Kohli scored 62 and six not out to move to 833 points, within 14 points of England's Joe Root in a list led by Australia captain Steve Smith.
Players from New Zealand and Australia made significant gains in the rankings updated after the first two matches of the ongoing series between the two sides.
England head to the Oval for the final Test of the summer against India on Thursday as the world's top side courtesy of a rankings system which is now widely accepted but not generally understood.
Veteran Sachin Tendulkar dropped out of the batting top-10 to the 13th spot, while pace spearhead Zaheer Khan slipped a spot to 10th in the bowling chart as India's misery in the Test series against Australia reflected in the latest ICC rankings issued on Sunday.
Virat Kohli remained the highest-placed Indian batsman at fourth even as Shikhar Dhawan rose a rung to sixth in the latest ICC ODI rankings.
KL Rahul leads a pack of India players who have shot up the MRF Tyres ICC Men's T20I Player Rankings after the visitors stormed to a 5-0 series win in New Zealand. Rahul's series topping aggregate of 224 runs has lifted him four places to a career best-equaling second place.
Veteran batsman Sachin Tendulkar and pace spearhead Zaheer Khan remained static at their respective 12th spots to be the highest-placed Indian cricketers in the latest ICC Test rankings issued on Wednesday.
With 762 points, Kohli is behind England's David Malan
The 28-year-old cricketer's ODI runs came at an average of 57.86 and an impressive strike rate of 95.15.
Another England bowler to advance in the rankings was Chris Woakes, whose five-wicket haul in the second innings lifted him to 20th position and a career-best rating points tally of 654.
Jasprit Bumrah, the fastest Indian pacer to 50 wickets, is now seventh in the bowlers' list after a leap of nine places owing to his five-wicket haul against the West Indies.
A win in 2nd Test vs New Zealand in Kolkata, can help India reclaim ICC Test C'ship mace
The ICC on Thursday came under attack for its "baffling" all-time Test player rankings which had no place for champion batsmen like Sachin Tendulkar and Brian Lara in the top 20 but the game's governing body made it clear that the list did not rank players in terms of true greatness.
India captain Mahendra Singh Dhoni is all set to lose his numero uno status in the ICC rankings for ODI batsmen after deciding to skip the triangular series in Zimbabwe starting on Friday.
Captain Virat Kohli stayed in third to be the best-placed Indian batsman in the latest ICC ODI rankings issued in Dubai on Friday.
India held on to their third spot, while Sri Lanka have retained their position as the number one ranked team after the annual update of the ICC Twenty20 Rankings was announced on Thursday.
The right-hander currently has 873 points in the list of Test batsmen, headed by Australia captain Steve Smith.
Sachin Tendulkar reclaimed the No 1 Test ranking after eight years following a successful run in the just-concluded Test series against Australia. Tendulkar was the highest run-getter with 403 runs in the two-match series, which India won 2-0.
Courtesy his 153-run knock against Australia in the Mohali Test, India opener Murali Vijay has jumped 16 places to career-best rank of the 43rd but Cheteshwar Pujara dropped out of top-10 in the latest ICC rankings for Test batsmen.
'Pakistan can beat any team on any given day'
Indian opener Gautam Gambhir capped a memorable 2009 by ending the year as the No 1 Test batsman in the ICC rankings issued on Thursday.
India's Virat Kohli may have flopped in the two innings of the first Test against England but the star batsman has held on to his second spot in the latest ICC ODI rankings released on Sunday.
The India right-hander has 862 points in his kitty, still 25 points behind AB de Villiers of South Africa, who is heading the list.
Brook, Gardner named ICC Players of the Month
Sachin Tendulkar remained the highest placed Indian batsman at his unchanged fifth position, while injured pacer Zaheer Khan held on to his sixth spot in the bowling chart of the latest ICC Test rankings issued on Sunday.
Pujara was placed sixth, down one rung, with 791 points, while Rahane occupied the ninth spot after slipping a couple of positions with 759 points.
The recent ODI tour of the Windies have cost the players their top slots.
India's batting sensation Cheteshwar Pujara climbed two places to the fifth spot, while Virat Kohli slipped a position to No 11 in the latest ICC Test rankings issued on Monday.
'I do not believe this has happened due to extreme aggression.'
India have extended their lead at the top of ICC Test rankings courtesy to second-placed Pakistan's defeat in the third and final Test against West Indies on Thursday. Kraigg Brathwaite and Shane Dowrich struck unbeaten half-centuries to guide West Indies to a first Test victory in 14 matches as the Caribbean side beat Pakistan by five wickets in Sharjah.
It isn't particularly surprising that India are right on top, say M J Manohar Rao and Srinivas Bhogle, as they deserve to be after winning the World Cup.
Kamalini's batting was all about precise placing and finding angles rather than power as England bowlers ran out of options against the left-hander.
Rishabh Pant on Wednesday overtook his superstar India teammate Virat Kohli to reach the sixth spot in the ICC Test rankings for batters.
Kohli (886 points) and Rohit (868 points) have gained two and three ratings points, respectively to occupy the top two positions in the batting rankings.
Lokesh Rahul, who hit two half-centuries in the deciding Dharamsala Test against Australia, on Thursday, jumped 11 places to a career-high rank of 11th in the latest ICC chart for Test batsmen.
Afghanistan's Rashid Khan, who took a wicket each in the three matches, conceding a total of 62 runs off his 12 overs, overtook Sri Lanka's Wanindu Hasaranga for the top spot.
Kohli's team-mates Shubman Gill, Mohammed Siraj and Kuldeep Yadav have also moved up in rankings.
The Indian cricket team's disastrous World Twenty20 campaign pushed it to third place in the ICC T20 rankings while this year's champion West Indies jumped five places to grab the second spot.
In the annual update, the results from 2011-12 were dropped from the calculations and outcomes from the 2013-14 series weighted at 50 per cent. Thus, India's heavy defeats against England and Australia in 2011-12 were no longer taken into account.
