Radwanska has won just one set of 17 she has played against Williams overall - in the 2012 Wimledon final. She has now dropped both round-robin matches in Istanbul, where she also lost to Williams in last year's semifinals. Williams is bidding for her fourth title in the event.
Errani also lost her opening group match on Tuesday to Azarenka and now looks all but certain to be eliminated.
Jankovic, who was ranked No. 1 in 2008 and is back in the top 10 for the first time since 2011, outplayed Azeranka to snap a four-match losing streak against a fellow former No. 1.
"Vika is a great champion, and I knew it was going to be a tough match. We played against each other in Cincinnati and I lost in three sets, and I think the difference today was that I was serving much better," Jankovic said.
Williams, 32, is enjoying the finest season in her career, having already won 10 titles. She added the French Open and U.S. Open titles to bring her Grand Slam record to 17 championships and is 75-4 for the year.
Williams, making her eighth appearance in the event, is looking to become the first player to successfully defend the title since Justine Henin in 2007. Henin was also the last to win 10 titles in a season, in 2007.
Williams has clinched the year-end No. 1 ranking for the third time in her career after 2002 and 2009
Li trailed 3-1 in the second set against Errani, but won the next four games. She twice attempted to serve for the match, first, wasting a match point at 5-3 and then again at 6-5. Despite trailing 3-1 in the tiebreaker, Li won the next five points and eventually converted her third match point when Errani sent a forehand into the net. That saw her take her head-to-head meetings against her Errani up to six wins without defeat.
"The first match is always tight," Li said, adding that she had felt rusty after a three-week break since her last tournament. "I still have to find the rhythm on the court."
The tournament brings together the top eight players in the world. They play two round-robin groups, with the top two finishers in each advancing to the semifinals.
Jankovic, now ranked No. 8 and seeded seventh because third-ranked Maria Sharapova pulled out of the event with a shoulder injury, proved to be the steadier player against Azarenka, the Australian Open champion.
"I was able to hold my serve and stay focused when I was serving and I waited for my chances to break, and she made some double faults at times and I took advantage of that," Jankovic said. "It's a great win for me, it gave me a lot of confidence."
The key game in the first set went to Jankovic after more than 10 minutes when she held serve for a 5-3 lead. Azarenka saved two set points in the next game but then sent a forehand wide on Jankovic's fourth in the 10th game.
Azarenka dropped her serve in the third game to fall behind and then held in the fifth despite serving three double-faults and facing four break points. But she could not trouble Jankovic on her serve and another forehand by Azarenka that sailed long to hand Jankovic the match.
"Of course she was playing well. I mean, I think she's playing her best tennis right now. Really improved a lot throughout the year, " Azarenka said. "But I cannot say that I played well and she was better today. Of course she was better today, but, you know, I let a lot of balls go. There were a lot of mistakes, small mistakes, a little bit bigger mistakes."
After losing the U.S. Open final to Serena Williams, Azarenka lost her opening matches in both Tokyo and Beijing before beating Errani on Tuesday.
Azarenka still has a 5-4 career edge over Jankovic.
