But former world number one Jankovic had to rally from a set down to notch up her first career win against ninth seed Petra Kvitova 6-7(7) 6-1 6-1.
The 32-year-old Williams, who will be eyeing her 10th title of the season on Sunday, received medical attention on her back during the second set but it provided no respite for Radwanska.
"Playing against Agnieszka, she plays like magic, she can move the ball left and right - she can do anything with her shots," Williams told reporters.
"So for me today it was just important to try to stay ahead of her, or one step ahead of her. I just tried to do that today and I'm happy with how things went."
Kvitova, who won her second WTA title of the year last week in Tokyo, edged Jankovic in the tiebreak to bag the first set but a flurry of errors in the second set handed the momentum back to the Serb.
"I lost to her the last two times we played. She has always given me a lot of trouble and didn't allow me to play my game," Jankovic told reporters. "Even today in the first set she was controlling the points.
"I was still there, but didn't feel comfortable. But in the next two sets I felt like I went on top of her and took control. Then as the match went on I think she got a little bit tired... and then I had everything in my hands, pretty much."
The Serb, who reached the top of women's world rankings in 2008, had no qualms in admitting that she had to be at her best to even have a chance against Williams, whom she has beaten four out of 10 times in the past.
"She's in unbelievable form. Even though I have beaten her in the past... I think she's the most difficult player to play against," Jankovic said.
"She has a lot of experience, winning a lot of titles and winning pretty much everything there is to win.
"She's physically so strong, I think stronger than 99 percent of the players. She has all the shots. When she's on top of her game, it's very difficult to beat her."
(Reporting by Sudipto Ganguly in Mumbai, editing by Pritha Sarkar)
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