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Peer won 6-2, 5-7, 6-4 in a first-round match that lasted two-and-a-half hours.
Eighth and ninth seeds Marion Bartoli and Sybille Bammer enjoyed a much easier day, winning through to the second round with identical scores of 6-2, 6-3 over Tathiana Garbin and Maria Kirilenko respectively.
Likhovtseva was ranked 15th in the world eight years ago but, after two seasons dogged by illness and injury, has slid down to number 49.
The 31-year-old Russian, who had to fight her way through the qualifiers at this Wimbledon warm-up event, suffered another thigh injury on Tuesday when she skidded across the grass into the semi-splits in the second game of the second set.
She soldiered on, saving six breakpoints in a long third game that went 10 times to deuce, before taking advantage of a dip in form by the Israeli world number 16 to go 4-1 ahead.
Peer came back to 5-5 but was broken to love in the 12th game to allow Likhovtseva to take the set.
The Russian took time out for medical treatment at the start of the third set and returned to court with strapping on her thigh. She looked likely to pull off a brave win when she broke twice to go 4-0 up but allowed Peer to level the score again and then surrendered her own serve to love in the 10th game.
MEEKLY SURRENDERED
Peer, a quarter-finalist at the Australian Open in January, will now play Japan's Aiko Nakamura who beat Aravane Rezai of France 6-1, 6-4.
Bammer will face Czech Lucie Safarova after knocking out Russian Kirilenko on a windy Centre Court.
Austrian Bammer was 5-1 up in the second set before Kirilenko, ranked 21 places below her in the world at 43rd, staged a late fightback.
The 20-year-old Russian saved a matchpoint with a forehand winner in the seventh and then broke Bammer as the Austrian served for the match.
Kirilenko's comeback was shortlived and in the next game she meekly surrendered a second matchpoint with a double fault.
France's Bartoli is ranked only three places above Italy's Garbin but had a surprisingly one-sided win and will now meet British wildcard Melanie South.
The top seeds at Eastbourne had first-round byes and enter the fray on Wednesday.
World number one Justine Henin will play Poland's Agnieszka Radwanska, who beat American lucky loser Jill Craybas 6-2, 5-7, 6-0 on Tuesday. Wimbledon champion Amelie Mauresmo will open against Italian Mara Santangelo, a 7-6, 6-3 winner over Ai Sugiyama of Japan.
