Serena Williams survived an injury scare to make a winning start in her bid to cap a brilliant comeback season by regaining the WTA Championship title in the tour's season-end event.

The Wimbledon, US Open and Olympic champion appeared to pull a gluteal muscle in the first set while attempting a vigorous retrieve, but played through the discomfort to overcome Angelique Kerber, a debutant in this top eight event.

Williams' tenacious efforts eventually earned her a 6-4 6-1 revenge over the improving German left-hander, who upset the American tennis legend in their last meeting, at Cincinnati two months ago, and who had her moments early on Tuesday too.

Kerber was surprisingly aggressive while coming back from 0-3 to 3-3 in the first set, and also played some good rallies while earning three chances to reach 5-5.

But she could not convert any of them, and once Williams broke for 3-1 in the second set with a trademark ferocious drive volley, the match quickly slid away from the woman from Kiel.

At the end Williams' celebrations seemed subdued, and it was an hour before she appeared for a press conference. She has little time in which to recover from any after-effects for on Wednesday she is scheduled first on against Li Na, the former French Open champion from China.

Kerber must now create a surprise if she is to retain any hopes of reaching the semi-finals, as her next group match is against the world number one, Victoria Azarenka, also on Wednesday.

Earlier the chances of the title changing hands increased significantly when Petra Kvitova, the defending champion, produced a downbeat and error-prone performance to lose 6-3 6-2 to Agnieszka Radwanska, the Wimbledon finalist.

It was the first time in four meetings that the Czech had lost to the Pole.

Later Kvitova appeared tearful and upset both by her performance and the result, admitting that her sadness and anger had increased after returning to the locker room.

"I was not very comfortable on court and I didn't feel pretty well," said the woman who had basked in some of her happiest moments here last year.