Cornet managed to get only 47% of her first serves in as she was broken three times as Radwanska looked set to continue her fine run at her home tournament.
However, despite only managing to improve her first serve to 55%, the Frenchwoman managed to secure the second set 6-2.
Radwanska raced into a 3-0 lead in the decider and was at game point to take a 4-0 lead but Cornet managed to level things at 3-3 and then at 4-4 secure the decisive break.
Results from the Katowice Open Women's Singles semi-finals
Camila Giorgi (Italy) beat 3-Carla Suarez Navarro (Spain) 7-6(2) 6-4
4-Alize Cornet (France) beat 1-Agnieszka Radwanska (Poland) 0-6 6-2 6-4
Results from the Copa Bogota Women's Singles semi-finals
5-Caroline Garcia (France) beat 6-Vania King (U.S.) 6-2 6-4
- Sports & Recreation
- Carla Suarez Navarro
- Camila Giorgi