Farzami opened her campaign with a 7-5, 6-3 victory over Uzbekistan’s Sevil Yuldashova.
After edging a closely contested first set, Farzami tightened her grip on the match and closed out the second set 6-3 to book her place in the next round.
Safi also produced a commanding performance, dispatching Tajikistan’s Shakhzoda Asimova 6-0, 6-1.
The Iranian dropped just one game throughout the match, taking the opening set without surrendering a game before completing a dominant straight-set victory.
Safi has previously made history as the first Iranian woman to win a Grand Slam match, while the ITF lists her career-high singles ranking as No. 1360.
Meanwhile, Rahmani and Yazdani suffered a 6-4, 6-4 defeat to China’s Fumin Jiang and Tianhui Zhang in the men’s doubles first round.
The Iranian pair stayed level with their Chinese opponents at 4-4 in the opening set, but Jiang and Zhang won the final two games to take the set 6-4.
Rahmani and Yazdani then made a fast start in the second set, moving 2-1 ahead, but the Chinese duo turned the momentum around and built a 5-3 lead.
Iran pulled one game back to narrow the gap to 5-4, but Jiang and Zhang held their nerve in the following game to seal another 6-4 set and complete the straight-set win.