Serena to face Jankovic in semifinal in Istanbul
Li and Kvitova are tied 3-3 in career meetings.
Azarenka's loss meant Jankovic advanced to the semifinals before she played Sara Errani later Friday. Errani won that match 6-4, 6-4.
Azarenka hurt her back while serving in the sixth game of the first set and was clearly in pain the rest of the match. The second-ranked Australian Open champion took a medical timeout and received treatment during several changeovers. She stayed on court despite poor movement.
"I just wanted to try to do my best for the fans who came and watched our match, for respect for my opponent," she said. "It was just about trying to do the most you can out there."
Li won the group 3-0, while Azarenka finished 1-2.
Despite failing to reach the semis, Azarenka said she was pleased with her year.
"I'm No. 2 in the world. I had great results in the big tournaments and I had injuries," Azarenka said. "So, it's that balance of good and unfortunate. I think I can learn a lot from these little things to prevent maybe some of the injuries."
Azarenka did win one game with some ferocious serving, but mostly stayed in the middle of the baseline and tried to hit quick winners.
"It's my decision what I'm going to do," Azarenka said.
Azarenka said her back suddenly seized up as she tried to serve hard and the trainers told her there was no structural damage.
Li lost to Azarenka in the final of the Australian Open and in both previous round-robin matches at the WTA Championships 2012 and 2011.
"I thought maybe after the first set she will give up or retire. ... I think it's tough because I have to focus," Li said.
In the Australian Open final, it was Li who was in trouble. She twisted her ankle and hit her head in a stumble before losing in three sets.
"Next time, we both have to be healthy on the court," Li said.
Although she did not play, Williams did appear on court to collect the award for finishing 2013 with the No. 1 ranking. Williams clinched the year-end top ranking for the third time, the others in 2002 and 2009.
Copyright 2013 by The Associated Press
This story is from ESPN.com's automated news wire. Wire index
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