Stuart Broad's figures of three for 38 and three for 28 have helped him gain two spots and move to 12th place, the position on which he had started the series while Chris Woakes has gained one spot to reach 34th place after taking four wickets in the match.
Among their batsmen, Jos Buttler is the biggest gainer, as his player of the match effort of 80 not out has lifted him 19 places to 63rd position.
Opener Alastair Cook (up one place to 13th), Dawid Malan (up one place to 60th) and Dominic Bess (up 23 places to 92) are the others to gain.
For Pakistan, Mohammad Abbas and Mohammad Amir have retained their 20th and 32nd places respectively, while leg-spinning all-rounder Shadab Khan has moved up three places to 93rd among bowlers and 22 places to 108th among batsmen.
Seam bowler Faheem Ashraf (up 18 places to 98th) and middle-order batsman Haris Sohail (up two places to 77th) are the other gainers in the latest rankings.
Seventh-ranked Pakistan could have swapped places with fifth-ranked England had they managed to win the second Test but the result means there are no change of places on the ICC Test team rankings with England losing one point and Pakistan gaining one.
In a series starting on Wednesday, the Windies play three Tests against Sri Lanka at home, with a chance to improve their position in the team rankings.
A 2-0 or verdict could help ninth-placed Windies overtake Bangladesh while pulling Sri Lanka down from sixth to seventh position.
ICC Test rankings:
1. Steve Smith (Aus) - 929
2. Virat Kohli (Ind) - 912
3. Joe Root (Eng) - 855
4. Kane Williamson (NZ) - 847
5. David Warner (Aus) - 820
6. Cheteshwar Pujara (Ind) - 810
7. Dean Elgar (SA) - 784
8. Aiden Markram (SA) - 759
9. Hashim Amla (SA) - 726
10. Dinesh Chandimal (SL) - 722
1. Kagiso Rabada (SA) - 897
2. James Anderson (Eng) - 892
3. Vernon Philander (SA) - 845
4. Ravindra Jadeja (Ind) - 844
5. Ravichandran Ashwin (Ind) - 803
6. Pat Cummins (Aus) - 800
6. Morne Morkel (SA) - 800
8. Trent Boult (NZ) - 795
9. Rangana Herath (SL) - 777
10. Neil Wagner (NZ) - 765
1. Shakib Al Hasan (Ban) - 420
2. Ravindra Jadeja (Ind) - 390
3. Vernon Philander (SA) - 371
4. Ravichandran Ashwin (Ind) - 367
5. Ben Stokes (Eng) - 327