The fierce rivals, who have been slugging it out with each other at the top of the world rankings for the last few years, are expected to meet each other in Friday’s final of the prestigious PSA event in London.
Both are going for a fourth title, with Sheffield-born Matthew having lifted the trophy for the last three years.
The 32-year-old world No 2 admitted he was lucky to have reached the last eight, however, after being forced to go 70 minutes with Colombia’s improving Miguel Angel Rodriguez, coming from behind to eventually prevail in their first round encounter 9-11, 11-8, 11-6, 11-9.
Matthew now faces South Africa’s Stephen Coppinger in Wednesday night’s quarter-finals at the East Wintergarden venue, roughly two hours after Leeds’s Willstrop takes on fellow Englishman Daryl Selby.
“Miguel was the better player and I was lucky to get through,” admitted Matthew. “I knew what to expect after our massive match in America last year and he has obviously come on a lot since then.
“I was fortunate with a few lucky bounces at crucial times and I am very relieved to get off the court with a win.
“He is so quick that sometimes you are just not sure if the ball is up or not. It was great entertainment and very enjoyable for the crowd, but not for me,”
Coppinger booked his place in the last eight defeating former Chapel Allerton regular Alister Walker in three games and was glad to see Matthew worked hard in his first round match.
“I am looking forward to playing Nick in the quarters and want to thank Miguel for giving him such a tough match,” said Coppinger.
Willstrop will go into his match against Selby refreshed after a rest day which followed Monday night’s four-game win over Charles Sharpes.
Selby will perhaps have been more glad of the rest day after being pushed hard over five games and 85 minutes by Germany’s Simon Rosner in their opening day clash.