Federer reeled off 13 games in a row to dig himself out of trouble and beat Russia's Nikolay Davydenko 2-6, 6-3, 6-0, 7-5 in a wildly fluctuating match.
Serena was also staring down the barrel in her quarter-final against Victoria Azarenka of Belarus before she recovered to beat Victoria Azarenka 4-6, 7-6, 6-2.
Her elder sibling might have joined her but threw away a match-winning lead in her 2-6, 7-6, 7-5 loss to Li, one of two Chinese women through to the last four at Melbourne Park.
Federer made it through to his 23rd consecutive grand slam semi but only after a titanic struggle with Davydenko, who won the opening set then got an early service break in the second.
The world number one was struggling just to stay with Davydenko as the sun started setting and shadows started creeping on to the Rod Laver Arena but seized his opportunity when the Russian suddenly went off the boil.
"I've played him many times and I know he goes through phases, you just try to stay positive," the Swiss said.
"I wasn't playing terribly, just struggling with the sun coming across. It's like a rain delay, you just wait."
Federer's next opponent will be either Novak Djokovic or Jo-Wilfriend Tsonga, who met in the 2008 Australian Open final, the only grand slam since the 2005 French Open where Federer has not been in the final.
SERENA COMEBACK
Serena showed why she remains the toughest woman in the world to beat, battling back from the brink of defeat to remain on course to defend the title she won for a fourth time last year.
The American lost the opening set to Azarenka then went behind 4-0 in the second as she started to doubt herself before she rediscovered her self-belief and found a way to win.
"I'm surprised. I didn't expect to win when I was down in the second set," she said.
"I thought if I lost the singles and the doubles, I could catch a flight Friday. It's not what a champion is supposed to think but I did."
Venus was two points away from wrapping up a straight-sets win when she stumbled on her serve and allowed Li back into the contest.
"In tennis you have to close it out. It's not like there's a clock ticking and then suddenly it's over," Venus said.
"You just have to close it out. I didn't do that today."
The once unimaginable prospect of an all-Chinese final is suddenly looming as a real possibility after Li followed Zheng Jie into the semis.
Zheng beat Maria Kirilenko 24 hours earlier and plays Justine Henin in Thursday's semis while Li faces the daunting prospect of playing Serena.
Millions of people in China have been following their matches on television and Li said she was adopting a philosophical approach to her match against Serena.
"In China we say if you have a tough time and then you return back, maybe you have good luck for after," she said. "So I still believe that."
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