Dushevina was beaten by Agnieszka Radwanska in the tournament finals last year and took a step back toward the title match with a 6-4, 7-6 (8-6) win over Szavay at the hard-court tournament.
Radwanska, the week's top seed, also won Wednesday, routing Mariya Koryttseva, 6-1, 6-1, while third-seeded Katarina Srebotnik defeated Anastasia Pavlyuchenkova, 6-3, 6-4.
In a first-round match, No. 6-seeded Sania Mirza beat Emilie Loit, 6-3, 6-2 and moved into a second-round pairing Thursday against Iveta Benesova.
Celebrity Couples of 2014 [PHOTOS]