Li, who won the inaugural title last year, lost her serve once while breaking Kichenok five times.
In the quarters, Li will play Monica Niculescu of Romania.
Klara Zakopalova, the Czech runner-up last year, bowed to Patricia Mayr-Achleitner of Austria 7-6 (2), 6-4 for the first time in three meetings. Mayr-Achleitner, up next against eighth-seeded Annika Beck of Germany, has a shot at her first semifinals since July 2011.
American Vania King earned her first win over a top-10 player when she upset No. 7-ranked Sara Errani of Italy 2-6, 7-6 (7), 6-3, despite losing her serve seven times. King awaited either Zheng Jie or Barbora Zahlavova Strycova of the Czech Republic.