Victoria Azarenka stayed on course for a first Wimbledon title and the world number one ranking by winning an engrossing Centre Court battle with Tamira Paszek.
The Australian Open champion booked her place in the semi-finals after being given a fright by Paszek, who put a half-season of woe behind her by triumphing on grass in Eastbourne before bringing that form with her to Wimbledon.
Eventually Azarenka negotiated her way past one of the few players in the women's capable of striking the ball with the same punishing force she applies, coming from a break behind in the second-set tie-break to advance 6-3 7-6 (7/4).
With Maria Sharapova ousted by Sabine Lisicki, who lost to fellow German Angelique Kerber, the top ranking in the women's game is up for grabs, with Azarenka and Agnieszka Radwanska the two players vying to leapfrog the Russian.
Azarenka looks to have the game on grass to go one step further than she managed last year, when she lost at the semi-final stage to Petra Kvitova.
Four-time champion Williams put Kvitova out today to show her own threat, but Azarenka may not be overpowered by the American.
She and Paszek traded fierce and often potent hitting, the Belarusian second seed and the unseeded Austrian giving the Centre Court crowd an unexpected treat as the match had initially been billed for Court One, only for rain to force the switch.
After fending off early pressure against her serve, Paszek was broken in the eighth game of the opening set as Azarenka fired an aggressive winner, and she consolidated that to take the set.
Serve ruled for the opening eight games of the second set, but then Paszek was broken to love.
Azarenka, serving for the match at 5-4, fell break point down and to her frustration then double-faulted, setting the pair back to square one.
The breaks kept coming, with Paszek conceding her next service game from 40-15 ahead, then rattling an unreturnable forehand to force the tie-break.
Paszek had the first mini break too, but Azarenka soon took charge, moving 6-3 in front and shrugging off the loss of the next point to a backhand winner as she clinched a last-four place when her opponent fired long.
"The games were really close," Azarenka said.
"At the beginning of the second set we were both doing well to hold our serves, then it turned around at the end with the breaks.
"It was difficult but I'm glad I could manage to win. It's a great feeling to be in the semi-finals of a grand slam but I still want to go all the way.
"It's still far away but I'm really glad to be in the semis here again and hopefully I can do better this year."
She knows of the threat posed by Williams, who has won seven of their eight past meetings.
"There's no better opponent than Serena in the semi-finals," Azarenka said. "I'm really looking forward to the match. It's not going to be easy but it's the semis of a grand slam so what do you expect?"