Thanks to reaching the Hobart final in January and the Acapulco semifinals last week, Benesova improved her ranking to No. 31 on Monday, surpassing the No. 33 she reached in 2005.
After starting off 3-0 down to Peer, Benesova cranked up her game and didn't give Peer another break chance, leading three more Czechs into the second round.
Barbora Zahlavova Strycova edged Anna-Lena Groenefeld of Germany 6-3, 2-6, 7-6 (4), and Petra Cetkovska beat Jarmila Groth of Slovakia 6-3, 6-2.
Second-seeded Marion Bartoli of France served five aces and won 72 percent of her first service points to take had an easy 6-2, 6-4 victory over Michaella Krajicek of the Netherlands. Bartoli will next play Romania's Edina Gallovits, who rallied to beat Magdalena Rybarikova of Slovakia 6-4, 3-6, 6-3.
Third-seeded Italian Flavia Pennetta, coming off the Acapulco final last weekend, swept past Jill Craybas of the United States 6-1, 6-0 in 56 minutes and will next meet Barbora Zahlavova Strycova of the Czech Republic in the second round.
Fifth-seeded Agnes Szavay of Hungary eliminated Pauline Parmentier of France 6-2, 6-2 and will next meet qualifier Vania King of the United States, who beat Klara Zakopalova of the Czech Republic 6-1, 6-4.
Other winners included Melinda Czink of Hungary, Mariya Koryttseva of Ukraine, and Roberta Vinci of Italy.
