The Pole capitalised on a below-par showing from her opponent to triumph 6-2 6-3 in Tuesday's second White Group match, which followed Caroline Wozniacki's epic three-set victory over world number two Maria Sharapova.
Radwanska had not played a competitive match since making an early exit from the China Open at the end of September.
Yet the world number six feels her previous experience of the WTA Finals - this is her fourth successive appearance at the season-ending event - proved significant in helping her to defeat Kvitova.
"I think I knew how to prepare for this tournament from other years," Radwanska is quoted as telling the tournament's official website.
"So I think I did everything right this year and I am really feeling good and ready to go.
"She's a great champion and playing some amazing tennis, especially the last few months, so I'm really happy with that win.
"There's only eight of us here, so you have to go out and try your best, otherwise you're not going to win. And I'm very happy with the way I played."
Kvitova - whose only previous defeat to Radwanska also came at the WTA Finals in 2012 - had been the favourite heading into the match.
Yet the Czech feels the quality of the field in Singapore means every contest is difficult to predict, highlighting Sharapova's earlier loss to Wozniacki as an example of the unpredictable nature of the event.
"I think probably we were both favourites in our matches and of course in our group," said Kvitova.
"That's what happens in tennis. I thought that I could beat Aga, but everybody is really up for this week and the matches can all go both ways."