Kvitova, the 2011 Championships winner and No. 5 seed in 2013, advanced with a 6-7 (3-7), 6-2, 6-3 victory over eighth-seeded Angelique Kerber in a win-or-go-home Green Group match. World No. 1 Serena Williams won the third of her round-robin matches Thursday to top the Green Group.
Li also went unbeaten in group play but, unlike Williams, did earlier drop a set. She had five breaks in the seven games Azarenka served. Li won two-thirds of the points serving and receiving Friday.
Errani finished off round-robin play with a 6-4, 6-4 decision over Jankovic, who had already earned a spot in the semifinals by virtue of Azarenka's straight-set loss and taking a set earlier from Li. Errani had three breaks in each set.
Jankovic, Azarenka and Errani all were 1-2 in group play but Jankovic advanced on a better set win-loss percentage.
Kvitova also had six breaks Friday, using two in the second set to even the match and three in the third to gain the semifinals.
Kvitova goes against Li in the first of Saturday's semis. They have split their previous six meetings.
Williams is 7-4 in her career against Jankovic in a series that began in 2004 and includes wins by Williams in the finals at Charleston, S.C., and Beijing this year.