He will meet Chinese snooker player He Guoqiang in the quarterfinals.
Vafaei had defeated English snooker player Oliver Brown 4-2 and Yuan Sijun of China 4-2 in his previous matches.
The competition runs from September 25 to October 1.
The Centaur at Cheltenham Racecourse hosts the third world ranking event of the 2023-24 season, with Ryan Day defending the Clive Everton Trophy against many of snooker’s biggest stars.
World No.1 Ronnie O’Sullivan has withdrawn from the tournament due to medical reasons.