CENTRE COURT -- 1:30 p.m. start
 Anastasija SEVASTOVA (LAT) vs.  Petra KVITOVA (CZE)
 Naomi OSAKA (JPN) vs. Donna VEKIC (CRO)
Not before 6:30 p.m.
 Kiki BERTENS (NED) vs.  Angelique KERBER (GER)
Not before 8:30 p.m.
Victoria AZARENKA (BLR) vs.  Anett KONTAVEIT (EST)
COURT 1 -- 2:00 p.m. start
Darija JURAK (CRO) / Raluca OLARU (ROU) vs. Anna BLINKOVA (RUS) / Oksana KALASHNIKOVA (GEO)
Not before 5:30 p.m.
[WC] Mona BARTHEL (GER) / Anna-Lena FRIEDSAM (GER) vs. Mandy MINELLA (LUX) / Andrea PETKOVIC (GER)
Anastasija Sevastova leads Petra Kvitova 2-1 in their head-to-head, but they have not played since 2011. Sevastova has now made the Stuttgart quarterfinals in her two most recent showings. She lost to Simona Halep in the final eight in 2017, in her last appearance at the event.
Kvitova is attempting to reach her third Stuttgart semifinal. She made that round in 2012 (lost to eventual champion Maria Sharapova) and 2016 (lost to eventual champion Angelique Kerber).
World No.1 Naomi Osaka and Donna Vekic have played once before, in the first round of the Australian Open in 2016, which Osaka won. Both players were ranked outside of the Top 100 when they contested that match.
Osaka's second-round win over Hsieh Su-wei was only the tenth clay-court main-draw win for the World No.1. This is also her first-ever clay-court WTA quarterfinal. Osaka is guaranteed to retain the World No.1 ranking coming out of Stuttgart.
The head-to-head between Kiki Bertens and Angelique Kerber is deadlocked at 2-2, and 1-1 on clay. Bertens had lost both of her previous matches at Stuttgart before this week, falling in the opening round to Svetlana Kuznetsova in 2017 and eventual champion Karolina Pliskova last year.
Kerber is a two-time champion at this event, having claimed the title in back-to-back years in 2015 and 2016. Since her first main draw appearance at the tournament in 2012, former World No.1 Kerber has gone 15-5 at the event.
Victoria Azarenka and Anett Kontaveit have played once before, with Azarenka taking that meeting in straight sets in the first round of Wimbledon in 2015.
Azarenka's second-round win on Thursday over defending champion Karolina Pliskova was her second victory over a Top 5 player this season, having defeated No.5 Kerber in the Monterrey semifinals. It was also her first win over a Top 5 player on clay since 2015 Rome (d. No.5 Wozniacki in the second round).