Mircic struggled in the first set, but came back a different player in the next, dropping only one game, and went on to win the second-round match 2-6, 6-1, 6-2.
Mircic will face third seed Tadeja Majeric, who beat Justyna Jegiolka 6-1, 6-3, in the quarterfinals of the ITF Women’s Circuit event.
“I started really poorly. Everything was just going really fast for me and she was hitting the ball really good and I couldn’t get ready for the ball,” said Mircic.
“In the second set I slowed her down, as her play didn’t suit me, so I just had to destroy her rhythm.
“The altitude is really tough for me, I’m still not used to it. The balls are really flying fast and hopefully for the next match I will try to swing my racket really tight and maybe it will be much better.”
Eighth seed Magda Linette of Poland was the victim of another upset as she lost 0-6, 6-4, 6-5 to Jade Windley of Great Britain.
Meanwhile, Simmonds continued her winning streak at the tournament when she beat compatriot Natasha Fourouclas 6-3, 6-2.
Simmonds now has tough hurdle to overcome in the quarterfinals where she comes up against second seed Julia Glushko who ousted Nicole Melichar 6-3, 6-3 in the second round.
“This was not an easy match for me,” said Simmonds.
“I’ve known Natasha for a long time. We train at the same academy.
"She’s a counter punch and she makes you work hard and makes you play, so I definitely had a workout today.
“But I served well today and hopefully I will be able to keep it up for my match tomorrow.”
Fourouclas remained positive despite the loss to Simmonds and said she would now focus on the rest of her season.
“I think I played well in the first set but lost it eventually, and towards the end of the second set I started to miss a little bit more and not play as much as I was,” said Fourouclas.
“I feel a bit disappointed. Chanel played very well so congratulations to her, but I’m going to move on, practice harder and look forward to doing well in the next tournament.”
Day three results for the women's Soweto Open, an ITF Challenger Tour event played at the Arthur Ash Tennis Complex in Jabavu, Soweto on Wednesday:
First round
Singles
7-Samantha Murray (GBR) bt Madrie Le Roux (RSA) 6-0, 6-1
3-Tadeja Majeric (Slo) bt Justyna Jegiolka (Pol) 6-1, 6-3
Teodora Mircic (Srb) bt 6-Jovana Jaksic (Srb) 2-6, 6-1, 6-2
1-Timea Babos (Hun) bt Pemra Ozgen (Tur) 6-2, 4-6, 6-1
4-Nadiya Kichenok (Ukr) bt Zuzana Zlochova (Svk) 6-1, 6-3
5-Chanel Simmonds (RSA) bt Natasha Fourouclas (RSA) 6-3, 6-2
2-Julia Glushko (Isr) bt Nicole Melichar (USA) 6-3, 6-3
Jade Windley (GBR) bt 8-Magda Linette (Pol) 0-6, 6-4, 6-4
Quarter-finals
Doubles
1-Magda Linette (Pol)/Chanel Simmonds (RSA) bt Tadeja Majeric (Slo)/Keren Shlomo (Isr) 6-1, 6-2
Samantha Murray/Jade Windley (GBR) bt 2-Basak Eraydin (Tur)/Julia Glushko (Isr) 6-4, 4-6, 10-5 MTB
Laura Pigossi (Bra)/Zuzana Zlochova (Svk) bt Claudia Coppola (Ita)/Marli van Heerden (RSA) 6-3, 6-3
3-Teodora Mircic (Srb)/Pemra Ozgen (Tur) bt Lynn Kiro (RSA)/Nathalia Rossi (Bra) 6-2, 6-2