Schiavone, seeded sixth in the tournament, edged Cornet 6-4, 6-4 in 2 hours 11 minutes.
One reason the match was so long was that Schiavone was 5-of-21 in break-point chances. Cornet was 3-of-9 but lost both of her break chances when Schiavone was serving for the match.
Schiavone improved to 9-1 lifetime versus Cornet.
Chanelle Scheepers posted her second win over a seeded player this week with a 6-1, 6-2 romp over No. 7 Kristina Mladenovic. Scheepers had six breaks, including four in the second set.
She beat second-seeded Sorana Cirstea in the first round.
Lourdes Dominguez Lino ousted fifth-seeded Kiki Bertens 6-4, 4-6, 6-3. She lost her serve three times in the third set but had five breaks as Bertens won only one-third of the points on serve in the set.
Mandy Minella gained the other semifinal slot, beating Silvia Soler-Espinosa 6-3, 3-6, 6-3 with six breaks.
Schiavone, who faces Scheepers in Saturday's semifinals, beat Scheepers in three sets in their only other career meeting. Dominguez Lino is 1-0 versus Minella, her semifinal opponent.