Williams, the top-seeded defending champion, will look to extend a dominant run through the women's draw against fifth-seeded Li Na of China, who became the first Chinese to reach the last four at the US Open.
Second seed Azarenka will face Italy's unseeded Flavia Pennetta, whose brilliant run at Flushing Meadows has carried her to her first grand slam semifinal.
Should form prevail, Williams and Azarenka would set up the first repeat final at the US Open since Serena Williams played her sister Venus Williams for the prize in 2002.
Azarenka, 24, joined the trio of 31 year olds with a last-eight victory over 30-year-old Daniela Hantuchova of Slovakia in a women's draw that has underlined the fitness and ferocity of the old guard.
Should they lift the trophy on Sunday, Williams, Li or Pennetta would become the oldest US Open women's winner since tennis turned professional in 1968, supplanting Australian Margaret Court, who was 31 years and 55 days old when she triumphed in 1973.
Williams has been on fire, losing only 13 games and spent the last time on court although she has done double duty playing with sister Venus in the women's doubles.
The American aced her quarter-finals test against Spain's Carla Suarez Navarro by delivering a 6-0 6-0 double bagel win.

Williams later offered a shuddering thought. "I like to believe there is always room for improvement," she said.
Against former French Open winner Li, current French Open champion Williams holds an 8-1 advantage in head-to-head meetings, but has had some hard battles along the way. She won their last encounter in Cincinnati 7-5 7-5 in the semis.
Williams holds the Chinese player in high regard. "She's a great challenge. She moves really well. She does everything well," Williams said.
"We've always played really close. Maybe next time we play she might want to go from close to a win," she said.
Li has been on a revenge tour, beating Briton Laura Robson to avenge a 2012 U.S. Open loss, and Serb Jelena Jankovic, who had enjoyed a four-match winning streak against her.
"It's a good challenge to play against her, because I think we always have tough match, even in Cincinnati," said Li.
"There are only four players at end of the tournament, so nothing you can worry about. Just play the tennis. Just enjoy the time," she said.
Azarenka and Pennetta have split their two previous matches, missing a crack at a rubber match when the Belarusian withdrew from their second-round Wimbledon contest this year because of a knee injury.


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