Cornet, seeded No. 3, defeated seventh-seeded Chanelle Scheepers 6-3, 6-1 by amassing seven breaks. Cornet won nearly two-thirds of the points when receiving serve and won in a lopsided score despite dropping serve three times.
The decision left Cornet as the only seeded player in the tournament.
Bouchard beat Anna Tatishvili 6-3, 6-2. She saw just two break points and won half the points when receiving serve.
Cornet and Bouchard will face off in Friday's semifinals -- their first WTA meeting.
The other semifinal will be determined in quarterfinals that were rained out Thursday. Flavia Pennetta was to play Misaki Doi and Lucie Hradecka was scheduled to meet Johanna Larsson. Those matches are set for early Friday, with the winners advancing to the second semifinal match.
Thursday was the second time the tournament schedule was affected by rain. Monday's entire schedule was washed out because of storms in the area.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut