Williams will face China’s Cao Yupeng in the quarterfinals.
Vafaei had defeated English snooker player Matthew Selt 4-3 in his opening match.
The event features a total prize fund of £380,000, with the winner receiving £100,000.
The tournament is taking place from January 15 to 21 at the Morningside Arena in Leicester, England.
It features the top 32 players in the one-year ranking list as it stood after the 2023 Scottish Open.