The Englishman outfought Vafaei 6-2 and reached the last 16 of the event.
World number 36 Vafaei had taken a 2-1 lead but Selby took five in a row, including a prolonged fourth frame and the seventh on the black for victory.
Selby, who won the title in 2012 and 2016, will face his fellow countryman Barry Hawkins in the next round.