Flipkens, who is ranked 66th and had to qualify for the main draw, trailed 3-1 before winning 11 of the next 12 games.
"It's incredible that I've beaten her," Flipkens said. "I tried to play my own game and switched a lot between attacking and defensive shots. Then Ana started to make more mistakes. I think that was because of the way I was playing."
Ivanovic won the tournament in 2008 and 2010. Flipkens, who won her first title in Quebec City last month, will play Goerges for a place in Sunday's final.
Azarenka reached her 10th semifinal of the season by defeating Petra Martic of Croatia 6-2, 6-2. Azarenka won the first 10 points to help build a 4-0 lead before Martic clawed her way back. The Croat had a break in the second set to make it 2-2 but did not win another game.
"I feel like I adjusted really well," said Azarenka, who had never played Martic before.
Azarenka has not dropped a set in 11 consecutive matches. She won in Beijing last week and pulled out in the quarterfinals at Tokyo the week before.
"Every day I have to push myself," Azarenka said. "It's not easy, even when it seems easy out there on court."
Azarenka will next play Begu, a Romanian who defeated Bethanie Mattek-Sands of the United States 6-4, 1-6, 6-2.
The match was interrupted in the second set for about 20 minutes after rainwater leaked from the roof onto the court.
The 57th-ranked Begu, who won her first career title in Tashkent last month, lost in qualifying but entered the main draw as a replacement for Anna Tatishvili of Georgia.
Goerges, who hasn't lost a set this tournament, beat Sofia Arvidsson of Sweden 6-1, 6-4. From 1-1 in the opening set, the German won seven straight games. Arvidsson broke back to tie it 4-4 in the second but then dropped her serve for the fourth time.