Top 2 seeds bounced in Budapest
Russia's Valeria Solovyeva routed top-seeded Safarova of the Czech Republic 6-1, 6-0, while fellow Czech Andrea Hlavackova was a 6-4, 6-2 winner against France's Cornet, who won the event in 2008.
Just a month ago, record flooding of the Danube River, which flows just a couple hundred yards from center court, threatened to cancel the tournament.
The venue was spared thanks to a dam built in 2006, but the surrounding neighborhood was under water for days. Ground water seeped into the courts but organizers were able to clean up and repair the damage in time for the tournament.