Wawrinka overcame mid-match struggles to defeat Martin Klizan 6-4, 0-6, 6-4 and set up a quarterfinal meeting with Reda El Amrani.
El Amrani, playing in his first ATP tour event of the year, defeated Jan Hajek 6-3, 2-6, 6-2.
Hanescu won over Jarkko Nieminen 2-6, 6-3, 6-2 and Gasquet was a 6-1, 6-1 winner over Andrey Golubev.
The other quarterfinal matches were determined Wednesday. Potito Starace will meet Lukasz Kubot and Florent Serra will take on second-seeded Guillermo Garcia-Lopez.
Millions of Getty images now available for free via embed tool
NBC reportedly holds celebs hostage to Jimmy Fallon's show