Barthel ousted fifth-seeded Roberta Vinci 4-6, 6-1, 6-3, facing only one break point after the first set. Barthel dropped just two points on serve in taking the second set and won 60 percent of the service points in the final set, even though she dropped serve once.
She'll face third-seeded Marion Bartoli in the quarterfinals. Bartoli Wednesday got past Christina McHale 7-5, 6-1. She had two breaks in each set. She dropped only 10 points in the second set, winning 80 percent of the points on serve.
Second-seeded Petra Kvitova defeated Stefanie Voegele 7-6 (7-5), 6-3 in the day's final match. Kvitova lost her serve three times but only once in the second set when she fought off five break chances.
No. 6-seeded Lucie Safarova rallied to a 2-6, 6-1, 6-1 win over Lourdes Dominguez Lino in a first-round match.
In the final first-round matches Wednesday, Magdalena Rybarikova slipped past Virginie Razzano 6-4, 3-6, 6-3 in a match that took 2 hours, 47 minutes; Kiki Bertens stopped Tamira Paszek 6-4, 7-5; and Yanina Wickmayer was a 7-6 (9-7), 4-6, 6-3 winner over Anastasia Pavlyuchenkova.
Swim Week Miami Beach 2014 [PHOTOS]