The Sheffield-born 36-year-old proved to be a class above the world no 13 as he made the most of difficult, humid conditions to recover from dropping the first game to secure the win after just over an hour of play.
“I was gearing up for a worst cast scenario and going 2-0 down when he took that second game lead,” said Matthew.
“That second game was crucial and maybe a turning point. I certainly felt more in control after that game - it settled me down a bit. “I felt a little bit flat for some reason when I first came on and I have to work out why that is. “The conditions were much harder tonight as well, it was windy and there was a little bit of humidity. But at the World Championships you have to dig those results out and I think I will benefit a lot from this match tonight in terms of getting me back match-fit for the next round.”
Matthew will now face Egyptian world No 3 Karim Abdel Gawad tomorrow for a place in the semi-finals.
Egypt has became the first nation in the entire 40-year history of the event to have six players in the quarter-final stage after Ramy Ashour, Fares Dessouky and Tarek Momen all won in the bottom half of the draw on Monday.
Ashour led the charge as he dispatched England’s Daryl Selby by an 11-6, 8-11, 11-5, 11-6 margin, while Dessouky came through a gladiatorial five-game battle with Malaysia’s Nafiizwan Adnan, winning 13-11, 6-11, 11-6, 10-12, 11-6.
Momen was also forced to battle through a five-game encounter after he dispatched World No7 Marwan ElShorbagy, the younger brother of World No 1 Mohamed, their 78-minute encounter finishing 11-9, 9-11, 11-8, 9-11, 11-3 in Momen’s favour to set up a quarter-final meeting with defending champion Gregory Gaultier.
2016 PSA Men’s World Championship - Third Round:  Mohamed ElShorbagy (EGY) bt Karim Ali Fathi (EGY) 3-0: 11-3, 11-6, 11-9 (36m);  Ali Farag (EGY) bt  Miguel Angel Rodriguez (COL) 3-1: 11-4, 6-11, 11-9, 11-7 (56m);  Karim Abdel Gawad (EGY) bt  Max Lee (HKG) 3-1: 7-11, 11-3, 11-6, 11-6 (49m);  Nick Matthew (ENG) bt  Simon Rösner (GER) 3-1: 6-11, 11-9, 11-7, 12-10 (65m);  Fares Dessouky (EGY) bt Nafiizwan Adnan (MAS) 3-2: 13-11, 6-11, 11-6, 10-12, 11-6 (99m);  Ramy Ashour (EGY) bt Daryl Selby (ENG) 3-1: 11-6, 8-11, 11-5, 11-6 (66m);  Tarek Momen (EGY) bt  Marwan ElShorbagy (EGY) 3-2: 11-9, 9-11, 11-8, 9-11, 11-3 (78m);  Gregory Gaultier (FRA) bt Tsz Fung Yip (HKG) 3-0: 11-8, 11-2, 11-6 (31m)
Quarter-Final draw (played November 11)
 Mohamed ElShorbagy (EGY) v  Ali Farag (EGY)
 Karim Abdel Gawad (EGY) v  Nick Matthew (ENG)
 Fares Dessouky (EGY) v  Ramy Ashour (EGY)
 Tarek Momen (EGY) v  Gregory Gaultier (FRA)