The seventh-seeded Potapova beat Kontaveit for the first time after two losses, including last week’s semifinal match at Hamburg. Potapova also reached the last four at Lausanne.
The Russian-born Potapova broke the Estonian five times as she raced to victory in 49 minutes. She has not lost a set at the hard-court tournament.
The 17-year-old Noskova advanced to her first career WTA semifinal after her opponent, Japan’s lucky loser Nao Hibino, retired when trailing 6-3, 4-2.