Rain Thursday washed out four second-round matches, which organizers rescheduled for Friday ahead of four quarterfinals.
Johansson started her day with a 6-2, 3-6, 6-2 victory over Shahar Peer despite 14 double faults. However, she had seven breaks of Peer's serve.
Johansson came back later and grabbed a 6-4, 6-0 decision over fifth-seeded Anastasia Pavlyuchenkova using a quick second set to complete the win in 57 minutes. Johansson dropped serve just once in the quarterfinal while cashing in all five of her break opportunities against Pavlyuchenkova.
Her semifinal opponent Saturday will be local favorite Johanna Larsson, who also had two wins Friday. Larsson knocked off third-seeded Anabel Medina Garrigues 6-4, 6-4 behind five breaks in her first match and was up 2-0 in the second when sixth-seeded Klara Zakopalova retired. Zakopalova also played twice Friday.
No. 7-seeded Mona Barthel defeated Sofia Arvidsson 6-3, 6-4 and Polona Hercog was a 3-6, 7-5, 6-4 winner over Tsvetana Pironkova in the other quarterfinal.
Saturday's semifinal will mark the first time Barthel and Hercog will have played each other. Larsson was a three-set winner the only time she played Johansson.