King pulled off a 6-3, 7-5 triumph over this year's French Open semifinalist to reach her first quarterfinal of 2011. It's only the third time King has won two matches in a single tournament this year. The other two occurrences came at the French Open and U.S. Open, and she was quickly ousted in the third round each time.
Bartoli, who had beaten King in the opening round at Brisbane back in January, has been eliminated by an American in the second round of each of her last two events. Christina McHale bounced the Frenchwoman out of the U.S. Open in round two a few weeks ago.
Other second-round winners Wednesday included fourth-seeded Dominika Cibulkova of Slovakia and fifth-seeded Polona Hercog of Slovenia. Cibulkova had won the first set in a tiebreaker, 7-6 (7-4), when qualifier Yaroslava Shvedova of Kazakhstan retired with a thigh injury, while Hercog posted a 6-3, 7-5 victory over Spain's Carla Suarez Navarro.
King and Zakopalova will meet in the quarterfinals, while Cibulkova and Hercog will square off on Friday.
The second round will continue Thursday with four more matches.
Russia's Vera Dushevina, fresh off an upset of top-seeded Italian Francesca Schiavone, will face Romania's Alexandra Dulgheru and Iveta Benesova of the Czech Republic will take on Kazakhstan's Galina Voskoboeva, who knocked out eighth-seeded Russian Ekaterina Makarova in the first round.
Also Thursday, sixth-seeded Spaniard Maria Jose Martinez Sanchez will battle Czech qualifier Kristyna Pliskova and third-seeded Julia Goerges of Germany will tangle with 2006 Seoul champ Eleni Daniilidou of Greece.
This week's champion will earn a first prize of $37,000.