Simmonds would now come up against Ukraine’s Nadiya Kichenok, seeded fourth, who edged out Great Britain’s Jade Windley 2-6, 6-1, 6-1.
The 20-year-old headed into the next encounter against the fourth-seed as favourite after she beat the Ukrainian 6-3, 3-6, 6-1 at the Malaysia Open earlier this year.
“I’m proud to be the first South African to get to the semis. It’s a great thing for me but my ultimate goal is to win the tournament,” said Simmonds.
“My serve was not as good as yesterday, but I was sliding wide and hitting more spins.
“I just had to make her (Glushko) play today because it’s tough to be consistent against her because she works so hard.”
It was a topsy-turvy first set as both players broke each others serve, but Simmonds held on to win the set 7-5, surprising the second seed, who then became rattled.
Simmonds recognised her opportunity and took advantage of her opponent’s frustration.
“The first set was very up-and-down and I think I got in her head because she seemed very uneasy and irritated, and lost a lot of patience,” said Simmonds.
“In the second set, she was just swinging and trying to hit winners off the second ball and so I just had to keep it in and make her hit five or six balls and then she’d miss.
“In the beginning she had a bit more patience and there was more rallying.”