The 31-year-old American will be the oldest player ever to win the WTA title if she goes all the way, and a new champion earlier became certain when Petra Kvitova, the titleholder from the Czech Republic, withdrew, apparently with a virus.
Williams, the Olympic, US Open and Wimbledon champion, came through 7-6 (7/2), 6-3 against Li Na, the former French Open champion from China, in a tense, noisy, and surprisingly fraught affair in which she never seemed fully at ease.
Williams was 1-3 down, then let slip a break of serve, and was pegged back to 6-6 in the first set, before surviving the tie-breaker.
She then yelled and scrambled and battled her way through five deuces before winning a pivotal fifth game in the second set.
Her second win here was more a triumph of will than anything else, for she landed less than 50 percent of her first serves – so often her best weapon – dropped service games five times, and needed an hour and 50 minutes before she prevailed.
Williams reflected: “I lost serve today more often than all of Wimbledon. I was just thinking about it too much. I didn’t serve well yesterday (Tuesday) and I thought about it. I just need not to think.
“But to win with zero serve, compared with what I normally do is something I can take from the match.”
Certainly Li sometimes returned serve well, and often went for broke with fierce flat-hit drives, which made it hard for Williams to achieve an attacking dominance and often forced her to scramble.
But Williams’ unease may also have been caused by lack of match play – until Tuesday she had not competed at all in the six weeks since winning the US Open in New York – or perhaps even uncertainty about her fitness.
The racket-smashing incident occurred during a weird fourth game in which one of the finest servers in the history of the game delivered two successive double faults to go a break down.
Yet Williams is also one of the most resilient fighters, as well as one of the most dangerous of one-strike attackers, and these tough qualities helped see her through.
About the smashed racket, she said: “I guess I was angry and I wasn’t able to control myself. But sometimes I play better when I get angry.”
She may though need to play better in her remaining group match if she is to maintain her outstanding record against world number one Victoria Azarenka, who may be aching to atone for losing the US Open final from 5-3 up in the final set.
Kvitova meanwhile was not herself during the 6-3, 6-2 loss to Agnieszka Radwanska, the Wimbledon runner-up from Poland, in their opening group match Tuesday, ending it angry and tearful.
“After one rally I couldn’t breathe, I was shaking all the match, and my stomach felt really funny. If I’m not a hundred percent to compete with these girls at this level I know I can’t play.”
“I thought at first it was nerves, but normally nerves are gone after the first set. It went on all through the match, so then I thought there was something wrong. That’s why I have pulled out.”
She has been replaced by Samantha Stosur, the former US Open champion from Australia, who can still qualify for Saturday’s semi-finals if she wins the remaining two matches in the white group, against Maria Sharapova, the second seed, and Sara Errani, the French Open runner-up.