Melanie Oudin wins opener
Zheng helped fuel Chinese tennis after becoming the country's first player to reach a Grand Slam semifinal in Wimbledon in 2008, where she made history two years ago by winning the first doubles title.
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Although the 28-year-old Zheng hasn't fully recovered from a wrist surgery, she defeated the hard-hitting Russian. She is ranked No. 32.
"It's really good to be back on grass and I aim to be back in the top 20 again" Zheng said.
Babos, the No. 14 seed, was in a tight match 6-4, 4-6, 3-3 against Alison Riske, the American qualifier who reached the semifinals here two years ago.
Meanwhile Baltacha, the No. 15 seed, lost the first set 4-6 but was up 3-2 in the second against Kai-Lung Chang of Taiwan.
Copyright 2012 by The Associated Press