Kerber, ranked sixth in the world, broke Kudryavtseva 10 times, but dropped her own serve eight times to allow her Russian opponent to stay in the match.
The 20th-ranked Williams is playing in her first tournament since losing to Maria Sharapova in the third round of the Australian Open in January.
Jelena Jankovic overcame problems with her serve to claim a 2-6, 6-4, 6-4 win over Melinda Czink in the second round of the Mercury Insurance Open on Thursday.
Leander Paes and his partner Elena Vesnina stormed into the semifinals of mixed doubles competition after a straight set win over Paul Hanley and Alla Kudryavtseva in the Wimbledon here.
Four-time Wimbledon champion Serena Williams moved into the third round with an overpowering serving performance Thursday, hitting 10 aces in a 6-1, 6-4 victory over Hungarian qualifier Melinda Czink.
China's Zheng Jie set up a potential Wimbledon revenge mission against four-time champion Serena Williams as she eased to a 6-4, 6-2 second round victory over Canada's Aleksandra Wozniak on Thursday.
Top-seeded Daniela Hantuchova of Slovakia advanced to the quarterfinals of the WTA Bell Challenge tournament on Thursday with a 6-7 (4), 6-4, 6-3 win over Hungary's Melinda Czink.
Defending champion Alla Kudryavtseva advanced to the second round of the Tashkent Open, beating fellow Russian Vesna Dolonts 6-2, 7-5 on Tuesday.
China's French Open champion Li Na reached the second round at Wimbledon on Tuesday with a comfortable 6-3, 6-3 win over Russia's Alla Kudryavtseva.
Alla Kudryavtseva of Russia eliminated sixth-seeded Jill Craybas 7-5, 6-2 in the second round of the Bell Challenge on Wednesday.