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Second seed Li, French Open champion two years ago, moved into a match-up with France's Marion Bartoli, a former titleholder at the grass event on the English south coast.
The Li match was interrupted for nearly half an hour after a women spectator fell backwards while entering the stadium and had to be treated by first aid personnel.
Li said she passed the time-out in the locker room watching television.
"At least I'm still in the tournament," she said.
"For a first grass-court match it was pretty good. I'm looking forward for tomorrow and another tough match."
Li led fellow seeds to opening victories on a calm day at normally blustery Devonshire park. Number three Angelique Kerber beat Sorona Cirstea 6-4, 6-4 while 2011 Wimbledon champion Petra Kvitova stopped Monica Niculescu 6-4, 6-1.
Fifth seed Caroline Wozniacki, the former WTA number one, began her grass campaign with a win as she put out holder Tamira Paszek. The Austrian retired trailing 6-2, 2-2 with the same left thigh injury which last week forced her from Birmingham.
Paszek, who has won just one match since mid-January, reached the Wimbledon quarter-finals at the last two editions. But she is now in doubt for next week.
"I can't say really much about the injury just now, I just have to do a couple more scans and analyse with the doctor," said the number
29 defending champion.
"It's really, really painful. I'm going to try my very best to get ready for Wimbledon and try to be positive.
"It happened at 1-all, I stretched a bit too much on the backhand side and actually heard a huge noise, which isn't usually a good sign. It was a sudden pain and I immediately called the trainer.
"I actually won that game, played like three winners on one leg. I knew I wasn't going to be able to continue. I'm going to try my best to even go on court in Wimbledon, try to get ready.
"If not it doesn't work out, I'll try to get healthy after that and make a new start. There is nothing else I can do about it."
Wild card Elena Baltacha claimed a British victory, beating Czech Karolina Pliskova 7-5, 7-6 (7/3) while Taiwan's Hsieh Su Wei beat Briton Johanna Konta 6-4, 6-3.
Australian Bernard Tomic has recharged his form on grass, shaking off last week's hamstring concern to post a 6-3, 6-4 first round win over Briton James Ward.
The victory came one week after Tomic lost in the opening round at Queen's Club to German Benjamin Becker while nursing his injury.
That's all past history now for the 64th-ranked Tomic. "This was an important win, it's a big relief to get this one," he said. "I've been happy with my tennis in training over the last three or four days.
"The hamstring is 100 percent now, If I can get some more wins like this on grass, it will really help my confidence. I think I have a chance to do well again."
Tomic is playing the Wimbledon tuneup for the first time two years after reaching a quarter-final at the All England club.
The top Australian, who captured his first career title at Sydney in January, finally broke a three-match first round losing streak dating to Madrid in May.
Spain's Feliciano Lopez, twice a Wimbledon quarter-finalist, beat Finn Jarkko Nieminen 7-6 (7/3), 7-6 (7/5). Slovak Martin Klizan beat Victor Troicki 6-3, 6-2, and Ivan Dodig stropped Denis Istomin 6-3, 6-4.
Results from the second day of the ATP-WTA Eastbourne International (x denotes seeding):
Men:
First round:
Bernard Tomic (AUS) bt James Ward (GBR) 6-3, 6-4
Feliciano Lopez (ESP) bt Jarkko Nieminen (FIN) 7-6 (7/3), 7-6 (7/5)
Martin Klizan (SVK) bt Victor Troicki (SRB) 6-3, 6-2
Ivan Dodig (CRO) bt Denis Istomin (UZB) 6-3, 6-4
Radek Stepanek (CZE) bt Marinko Matosevic (AUS) 6-3, 6-2
Julien Benneteau (FRA) bt Kevin Anderson (SAF x5) 7-6 (7/4), 6-2
Women:
First round:
Hsieh Su-Wei (TPE) bt Johanna Konta (GBR) 6-4, 6-3
Lucie Safarova (CZE) bt Klara Zakopalova (CZE) 6-4, 7-6 (7/3)
Angelique Kerber (GER x3) bt Sorana Cirstea (ROM) 6-4, 6-4
Caroline Wozniacki (DEN x5) bt Tamira Paszek (AUT) 6-2, 2-2 retired
Elena Baltacha (GBR) bt Kristna Plskova (CZE) 7-5, 7-6 (7/3)
Petra Kvitova (CZE x4) bt Monica Niculescu (ROM) 6-4, 6-1
Li Na (CHN x2) bt Alize Cornet (FRA) 6-2, 6-4
Elena Baltacha (GBR) bt Karolina Pliskova (CZE) 7-5, 7-6 (7/3)
Ekaterina Makarova (RUS) bt Olga Puchkova (RUS) 6-3, 6-0
Laura Robson (GBR) bt Yuliya Beygelzimer (UKR) 6-3, 6-2
Samantha Stosur (AUS) bt Nadia Petrova (RUS x8) 6-2, 6-3
Jamie Hampton (USA) bt Agnieszka Radwanska (POL x1) 7-6 (7/2), 6-2
