Two-time champion Matthew, from Sheffield, saw off the challenge from Egyptian qualifier Zahed Mohamed by winning 11-5 11-4 11-4 in 39 minutes.
The 33-year-old fourth seed, who won the event in 2010 and 2011, will face Hong Kong’s Max Lee this afternoon after the 25-year-old defeated Halifax-based Jonathan Kemp 11-7 13-11 12-10.
Third seed Willstrop also progressed 3-0, winning 11-4 11-4 13-11 against Derbyshire’s Joel Hinds, who may have been slightly hampered by his gruelling victory in the final round of qualifying on Sunday when he beat fellow Englishman Chris Ryder 11-6 11-5 8-11 3-11 14-12 in 78 minutes.
Willstrop, a beaten finalist in 2010, will now take on Tom Richards, who took almost an hour to see off the challenge of fellow Englishman Ben Coleman 11-8 11-7 11-9.
Possibly waiting for Willstrop in tomorrow’s third round will be Spain’s Borja Golan, the ninth seed, who defeated Harrogate-based Chris Simpson 11-9 6-11 9-11 11-8 11-5 after a hard-fought 110 minutes to book a second-round encounter today with Mexican qualifier Cesar Salazar.
Undisputed world No 1 and pre-tournament favourite Ramy Ashour made it 46 PSA Tour games unbeaten, but had to come from behind to win 10-12 13-11 11-3 11-4 against Laurens Jan Anjema from the Netherlands in just over an hour.
No 2 seed Gregory Gaultier, who beat Matthew earlier this month in the final of the US Open in Philadelphia, also made it through, but was given a decent workout by Denmark’s Kristian Frost before prevailing 11-8 11-7 11-6.