Vafaei defeated Billy Joe Castle from England 6-3.
He will meet Englishman Michael Holt on Sunday.
Soheil Vahedi, another Iranian snooker player, lost to his Chinese opponent Haotyan Lyu 6-4 and was knocked out of the competition.
Ronnie O'sullivan, who has won the tournament seven times, more than any other player, is participating in the prestigious event.
Prize money
Winner: £200,000
Runner-up: £80,000
Semi-finals: £40,000
Quarter-finals: £24,500
Last 16: £17,000
Last 32: £12,000
Last 64: £6,500