Rahul, who has 743 points, and Australia all-rounder Glenn Maxwell have climbed a rung each to be placed sixth and seventh respectively.
Rahul and Kohli are the only two Indians to feature in the top-10 among batsmen. No Indian features in the top-10 among bowlers and all-rounders in the latest T20I rankings.
In the ODI rankings, Kohli and vice-captain Rohit Sharma remained in the top five, occupying the second and third spots respectively, behind Azam.
Indian pace ace Japrit Bumrah, the lone bowler from the country in the top 10, dropped a spot to sixth place, while Ravindra Jadeja remained in the ninth position in the all-rounders' list.
England all-rounder Chris Woakes reached a career-best third position among bowlers after a fine show against Sri Lanka in the three-match ICC Men's ricket World Cup Super League series.
Woakes, who grabbed six wickets in two matches, including a haul of four for 18 in the first ODI, has advanced four slots in the list led by New Zealand's Trent Boult with Bangladesh's Mehidy Hasan Miraz in second place.
Woakes' previous best was fourth position attained in September last year. He is also up one place to third among all-rounders after overtaking team-mate, Ben Stokes.
Other England fast bowlers David Willey and Tom Curran, too, have gained in the latest men's weekly rankings update.
Willey has moved up 13 places to 37th position after a 'Player of the Series' effort of nine wickets that included a haul of four for 64 in the second match, while Curran's four wickets in two matches saw him advance 20 places to 68th position.
England's 2-0 series win, which helped them to the top of the CWC Super League Standings also sees Test captain Joe Root move up two places to 13th position with a series-topping aggregate of 147 runs and white-ball skipper Eoin Morgan inching up from 26th to 25th.
In the men's T20I rankings, South Africa's Quinton de Kock has advanced nine places to 13th after aggregating 255 runs in their five-match series against the West Indies.
For the West Indies, Evin Lewis is up one place to ninth position after finishing with 178 runs. Nicholas Pooran has gained 20 places to reach 87th position while Shimron Hetmyer is up 15 places to 99th.
All-rounder Dwayne Bravo has moved from 95th to 44th among bowlers after finishing with 10 wickets in the series while Obed McKoy has moved up 65 places to 53rd with nine wickets.