Vafaei defeated Xintong Zhao from China 4-3.
The Iranian had started the competition with a 4-2 win over Englishman Peter Lines.
Vafaei will meet world number one Judd Trump on Thursday in the third round.
The 2021 Welsh Open is an ongoing professional ranking snooker tournament, taking place from February 15 to 21, 2021 at the Celtic Manor Resort in Newport, Wales.
The event's total prize fund is £405,000, with the winner receiving £70,000.