Top-seeded Agnieszka Radwanska of Poland failed to reach the second round of the Aegon International when she was beaten 6-4 3-6 7-6 (4) by Anastasia Pavlyuchenkova of Russia.
But defending champion Elena Vesnina of Russia held off a strong challenge to beat Shuai Peng of China 6-3 6-4, and there was another hard-fought victory for 2012 runner-up Angelique Kerber of Germany, who defeated Alison Riske of the United States 7-6 (6) 6-4.
Former champion Caroline Wozniacki of Denmark also won, beating Australian Samantha Stosur 7-5, 6-4.
Radwanska won the grass-court tournament in 2008, but she has since fallen in the first round four times and not won a match at Eastbourne since she reached the quarter-finals in 2011.
Despite her early exit, Radwanska was not too concerned about her lack of match preparation for Wimbledon.
In 2012 after a first-round defeat she went on to reach the Wimbledon final, and last year after an opening-round loss she reached the semi-finals there.
"The first match (on grass) is always tricky," she said.
"Well, it was a great match before Wimbledon to get used to it ... I just hope I can do the same good results (at Wimbledon) this year."
Wozniacki had to recover a break of serve at the beginning of each set to defeat Stosur but felt comfortable to be back on a surface which netted her the 2009 title at Eastbourne as well as the junior trophy at Wimbledon.
Following her first round defeat at Roland Garros, Wozniacki enjoyed a break in Miami with family and friends, including Serena Williams.
"That was a lot of fun," Wozniacki said. "Serena and I had a good time with some of our other friends ... I came back home and I worked hard every day four, five hours a day. My game is in good shape."
Eastbourne also features No.8 Victoria Azarenka of Belarus. A left foot injury restricted the former No.1 to just one match since she surrendered her Australian Open title in the quarter-finals in January.
Drawn to face Italian Camila Giorgi in her opening match on Tuesday, Azarenka said, "It's not important for me who's going to be on the other side. I just want to see what I can do, and just see how to raise my level from there."
Everyone's mind inevitably is on Wimbledon, which begins next week, but second-seeded Petra Kvitova, who reached the Eastbourne final in 2011 before going on to claim the Wimbledon title, is determined to keep her focus on this week.
"Of course, I want to play the best that I can to get used to the grass and everything before Wimbledon, but I'm taking this tournament as a very big one," Kvitova said. "It's a very tough draw. Everybody wants to be successful here."
In the men's event, Frenchman Jeremy Chardy beat former two-time champion Ivo Karlovic of Croatia 6-4 6-4, sixth-seeded Gilles Simon of France defeated Australian qualifier Chris Guccione 7-6 (2) 6-4 and American Sam Querrey beat Britain's Kyle Edmund 7-6 (5) 6-3.
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