Kanepi, seeded fifth this week, knocked off No. 3-seeded Sara Errani 6-2, 6-2 and Oprandi was a 7-5, 6-0 winner over second-seeded Aravane Rezai.
Oprandi won six of seven break-point chances and won 54 percent of the points on Rezai's serve.
Kanepi topped that, winning 60-percent of points when Errani was serving.
The other quarterfinals Friday saw top-seeded Flavia Pennetta defeat Nuria Llagostera Vives 6-4, 6-2 and No. 8-seeded Julia Goerges stop Jill Craybas 6-2, 6-4. Pennetta and Goerges each had six service breaks in their wins, as did Kanepi and Oprandi.
Pennetta and Goerges will meet in one of Saturday's semifinals while Kanepi and Oprandi play in the other.
2014: The Year in Music [PHOTOS]