Halep, playing in her first tournament alongside new coach Thierry Van Cleemput, ground out a 7-6 (1), 7-6 (6) victory in just over two hours on court.
The Romanian raced to a 4-0 lead in the opening set, only for Goerges to fight back and force the tiebreak. Germany's Goerges took control with an early break in the second but Halep responded powerfully to see out the win in straight sets.
No. 4 seed and wild-card Svitolina earlier recorded a comfortable 6-4, 6-2 win over Czech qualifier Karolina Muchova in their quarterfinal clash.
"[Muchova is] a very good player, and I really like her game style," Svitolina said of her opponent. "She's not as a typical young player, because most of the players now that are coming up, they are smashing the ball. She has lots of variety in her game, and that's very good for tennis."
World No. 49 Strycova needed only 30 minutes to take the first set 6-1, breaking Kerber twice along the way before the German sparked into life to dominate the second set and level. Kerber kept her nerve in a tense decider and sealed victory after a tense tiebreak. The No. 3 seed will face Elise Mertens for a place in the final, after the Belgian overcame No. 5 seed Kiki Bertens 6-4, 6-3.
"You never know what to expect, if she is playing serve and volley or just moving, playing fast," Kerber said of Strycova after her victory. "But you have to be ready for every single moment and playing every single point, because every single point is different, especially against her."