Kvitova, the 2011 champion, finished second behind the unbeaten Williams in the Red Group after unleashing 47 winners in her victory over fellow left-hander Kerber.
Jankovic went through to the last four despite losing 6-4 6-4 to Italian Sara Errani in the final White Group match.
World number two Azarenka was forced to take a medical timeout in the sixth game against Li and from then on she was only able to win one more game.
"Today the match was not about tennis, it was about fitness," Li told reporters. "It was a mental challenge because I thought maybe after the first set she would give up or retire but she still tried to continue.
"I could have lost the match because I could not focus on the court. I have to enjoy this moment but I hope the injury isn't too bad and she can come back soon."
Li will rise to number three in the world, the highest-ranking ever for an Asian player, if she reaches the final of the season-ending tournament.
Azarenka, who finished third in the White Group, said she carried on playing so as not to disappoint the crowd and out of respect to Li.
"I just wanted to try to do my best for the fans who came to watch and out of respect for my opponent," said the Belarussian. "It was just about trying to do the best I could out there."
Kvitova said she was looking forward to her semi-final with Li.
"I think it's going to be a big fight, a nice match for the people and for us too," she added. "It's going to be great tennis."
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- Serena Williams
- Jelena Jankovic
- Petra Kvitova
- Angelique Kerber