The third-ranked Zvonareva, who received a first-round bye, rebounded from a tough opening-round match to move into the quarterfinals. She will face No. 12 seed Sabine Lisicki of Germany, a 6-4, 6-3 winner over American teenager and local favorite Coco Vandeweghe.
Lisicki used two early service breaks to jump out in front 5-1 in the first set before Vandeweghe rebounded. The 19-year-old, who grew up less than 10 miles from the site of the tournament, fought back to within 5-4. Vandeweghe staved off two set points before Lisicki finally won the set on an 108 mph service winner.
"I didn't play my best tennis," Lisicki said. "The important point was that I pulled it through."
Lisicki, who beat Vandeweghe 6-1, 6-0 in their last match at the 2010 U.S. Open, broke her opponent early in the second set for a 3-1 lead. The German finished off the the match when she broke Vandeweghe again in the ninth game.
After a 6-4, 7-5 win in the second round Tuesday against American qualifier Jill Craybas, Zvonareva was pleased with her performance.
"I think I started off a little slow but then I think I picked it up and it was a little bit better, a little bit cleaner than the previous one," Zvonareva said.
With the score tied 2-all, Petkovic won seven straight games to win the first set 6-2 and jump ahead 3-0 in the second when France's Virginia Razzano retired with a right shoulder injury.
Radwanska dispatched one of the three remaining American teenagers with a 6-1, 6-0 win over 19-year-old Christina McHale.
Fifth-seeded Ana Ivanovic advanced to a quarterfinal match against No. 4 seed Peng Shuai of China with a 6-1, 6-2 win against Italy's Alberta Brianti. Peng had to come from a set down and rally from a 1-3 hole in the third set to beat No. 16 seed Sara Errani of Italy 4-6, 6-2, 7-6 (7).
Daniela Hantuchova, the No. 8 seed from Slovakia, beat Zheng Jie of China, 6-2, 4-6, 6-4 and will meet Radwanska in the quarters.
In the only match not involving a seeded player, U.S. teenager Sloane Stephens was ahead 5-3 and had a set point when Tamira Paszek of Austria retired with a left abdominal injury. The 18-year-old Stephens next faces Petkovic in the quarterfinals.
Radwanska, the runner-up here last year, saw improvement over her opening-round match when she was pushed to a tiebreaker in a straight-set win over Elena Baltacha of Britain.
"I was very happy with my performance," Radwanska said. "I think I played much better than the first match. Everything was working."
Petkovic was sailing through her match when Razzano pulled out with her injury.
"The first two games I think we were both playing really well," Petkovic said. "I managed to hold onto that level and I don't know if was her injured shoulder or neck, but afterward she dropped her level. I managed to stay at the top level."