Budapest, Hungary -- (Sports Network) - Hungary's Agnes Szavay was a first-round winner Tuesday in her home country at the GDF Suez Grand Prix tennis tournament.

The fourth-seeded Szavay rolled to a 6-1, 6-1 victory over countrymate Katalin Marosi.

Second-seeded Alize Cornet of France, third-seeded Austrian Sybille Bammer and fifth-seeded Russian Alisa Kleybanova were also winners Tuesday.

Cornet disposed of Kazakhstan's Galina Voskoboeva, 6-3, 6-1, while Bammer was an easy 6-2, 6-3 winner over Klara Zakopalova of the Czech Republic. Kleybanova also had little trouble in a 6-0, 6-3 rout of Romania's Monica Niculescu.

A pair of seeded players were eliminated by qualifiers Tuesday, as Switzerland's Timea Bacsinszky rallied from a set down to beat Italian seventh seed Sara Errani, 5-7, 6-4, 6-0, and Croatia's Petra Martic dumped eighth- seeded Lucie Safarova of the Czech Republic, 7-6 (7-5), 6-0.

Other winners Tuesday included Israel's Shahar Peer, Italy's Tathiana Garbin, Austria's Patricia Mayr, Romania's Ioana Raluca Olaru and a pair of Ukrainians in Mariya Koryttseva and Kateryna Bondarenko.

This week's top seed, Patty Schnyder of Switzerland, is set to play her first match on Wednesday against Germany's Andrea Petkovic.

The 2009 Budapest champion will collect $37,000.