Jet lag could not hold back Elena Rybakina as she gained revenge over Ekaterina Alexandrova in Rome on Monday.
Kristyna Pliskova ended Petra Martic's hopes of success in Prague, but the Croatian's fellow seed Elise Mertens was victorious in round two.
Top seed Petra Martic fell short against Anett Kontaveit in the Palermo Open semi-finals, while Italian hopes were dashed by a Frenchwoman.
Petra Martic and Anett Kontaveit are the last two seeds standing at the Palermo Ladies Open.
Petra Martic and Anett Kontaveit are into the last eight at the Palermo Ladies Open.
After a couple of tough weeks, Sofia Kenin came through her opener in Lyon against Vitalia Diatchenko.
Chloe Paquet dominated Kristina Mladenovic in the first set, but the second seed rallied to reach the second round in Lyon.
Three seeds exited the Pan Pacific Open on Thursday, as Misaki Doi continued her impressive form in her home country.
Kiki Bertens awaits at the Pan Pacific Open for Anastasia Pavlyuchenkova, who was a round-one winner in Osaka.
Camila Giorgi was in control of the deciding set, but ultimately fell to a late surge from first-time WTA Tour winner Magda Linette.