Williams dominated the second-set tiebreaker, clinching the match with an ace, after Li saved three match points in the 10th game and one in the 12th.
"I had so many match points and I blew it and I knew I couldn't mess up my serve because she never gives up," Williams said. "She's a real, real amazing fighter."
In the first tiebreaker, Williams picked up four of her last five points on unforced errors by Li and clinched the set with a second-service ace.
Williams has a perfect record in Melbourne Park finals, having won titles in 2003, 2005, 2007 and last year.
Davydenko unloaded everything he had on Federer for a set and a half and was suddenly in uncharted territory at a Grand Slam tournament.
That's when a bit of gamesmanship and a lot of big-match experience helped Federer switch gears and win 13 straight games en route to a 2-6, 6-3, 6-0, 7-5 victory.
Davydenko had lost 12 matches to Federer before gaining some confidence with his back-to-back wins.
After dropping the first set, Federer decided to take a quick comfort break to let the sun that had been bothering him move a little bit.
That gave Davydenko time to think about the situation at Rod Laver Arena.
It didn't work right away. Federer dropped serve three games later and fell behind 3-1, but then the momentum swung dramatically.
"You're allowed to have two toilet breaks and I never use them, and I figured maybe the sun goes by one centimeter to three centimeters ... maybe it's that one point that makes a difference," Federer said, adding for the record: "Oh, I had to go to the toilet, too."
The win stretched his record to a 23rd straight Grand Slam semifinal appearance, something he rated as "definitely one of the most incredible things I have in my resume." Before Federer, Ivan Lendl and Rod Laver shared the record at 10.
Djokovic complained of an upset stomach after a 7-6 (8), 6-7 (5), 1-6, 6-3, 6-1 loss to Tsonga, reversing the outcome of their meeting in the final here two years ago.
"I saw he wasn't very good, but sometimes he does that and he wins," Tsonga said.
Williamses opt for football
Serena and Venus Williams will not play in the Feb. 6-7 Fed Cup quarterfinal between the United States and France, saying they plan to be in South Florida for Super Bowl weekend in their roles as part owners of the NFL's Miami Dolphins. - AP