“It was nice to use my experience against Jack,” he continued.
Norrie has now defeated Draper three times, with the younger Brit still unable to win a set off his compatriot.
Norrie, ranked No 42, will play the winner of the match between American Marcos Giron and German Alexander Zverev, the No 4 seed, next.
Cameron Norrie won against Argentinian Facundo Diaz Acosta (7-5, 7-5, 6-3) in the previous round of The Championships.
During the first round of The Championships, Draper, ranked No 28, beat Swede qualifier Elias Ymer (3-6, 6-3, 6-3, 4-6, 6-3).
London (Grand Slam), other second-round results (All England Lawn Tennis and Croquet Club, grass, GBP 50.000.000, most recent results first):
- Marcos Giron vs. Alexander Zverev
- Giovanni Mpetshi Perricard vs. Yoshihito Nishioka: thursday
- Emil Ruusuvuori vs. Stefanos Tsitsipas: thursday
- Lucas Pouille (Q) beat Thanasi Kokkinakis: 2-6, 7-5, 5-2 ret.
- Taylor Fritz (13) beat Arthur Rinderknech: 6-3, 6-4, 3-6, 6-4
- Holger Rune (15) beat Thiago Seyboth Wild: 3-6, 6-3, 6-2, 6-2
- Quentin Halys (Q) beat Karen Khachanov (21): 4-6, 6-3, 3-6, 6-3, 6-4
- Gael Monfils beat Stan Wawrinka: 7-6 (5), 6-4, 7-6 (3)
- Alejandro Tabilo (24) beat Flavio Cobolli: 7-6 (4), 7-6 (4), 4-6, 4-6, 6-4
- Novak Djokovic (2) beat Jacob Fearnley (WC): 6-3, 6-4, 5-7, 7-5
- Roman Safiullin beat Tomas Machac: 6-2, 6-4, 5-7, 6-3
- Lorenzo Musetti (25) beat Luciano Darderi: 6-4, 4-6, 6-7 (5), 6-4, 6-4
- Alexei Popyrin beat Tomas Martin Etcheverry (30): 3-6, 6-4, 4-6, 6-4, 6-3
- Grigor Dimitrov (10) beat Juncheng Shang: 5-7, 6-7 (4), 6-4, 6-2, 6-4
- Denis Shapovalov beat Daniel Altmaier: 7-6 (3), 6-3, 1-6, 6-7 (3), 6-4
- Ben Shelton (14) beat Lloyd Harris (Q): 4-6, 7-6 (5), 6-7 (5), 6-3, 7-6 (7)
- Alex De Minaur (9) beat Jaume Munar: 6-2, 6-2, 7-5
- Arthur Fils beat Hubert Hurkacz (7): 7-6 (2), 6-4, 2-6, 6-6 (8) ret.
- Francisco Comesana beat Adam Walton: 7-5, 1-6, 6-7 (12), 6-1, 7-6 (8)
- Jannik Sinner (1) beat Matteo Berrettini: 7-6 (3), 7-6 (4), 2-6, 7-6 (4)
- Jan-Lennard Struff beat Zhizhen Zhang (32): 5-7, 6-3, 7-6 (1), 7-6 (8)
- Miomir Kecmanovic beat Tallon Griekspoor (27): 4-6, 7-6 (7), 1-6, 6-2, 6-3
- Tommy Paul (12) beat Otto Virtanen (Q): 4-6, 6-3, 5-7, 7-5, 6-4
- Roberto Bautista Agut beat Lorenzo Sonego: 6-3, 3-6, 6-3, 6-4
- Alexander Bublik (23) beat Arthur Cazaux: 6-4, 7-6 (1), 6-4
- Carlos Alcaraz (3) beat Aleksandar Vukic: 7-6 (5), 6-2, 6-2
- Daniil Medvedev (5) beat Alexandre Muller: 6-7 (3), 7-6 (4), 6-4, 7-5
- Ugo Humbert (16) beat Botic van de Zandschulp: 7-6 (9), 6-1, 6-3
- Brandon Nakashima beat Jordan Thompson: 6-3, 6-2, 6-2
- Frances Tiafoe (29) beat Borna Coric: 7-6 (5), 6-1, 6-3
- Fabio Fognini beat Casper Ruud (8): 6-4, 7-5, 6-7 (1), 6-3