He defeated Englishman Michael Holt 6-4 in Round 2.
Vafaei started the prestigious campaign with a 6-3 win over Billy Joe Castle from England in Round 1.
He will meet the winner of Mark Selby and Liam Highfield in Round 3 on Monday.
Ronnie O'sullivan, who has won the tournament seven times, more than any other player, is participating in the event.
Last 16: £17,000
Last 32: £12,000
Last 64: £6,500