MELBOURNE, Australia — Novak Djokovic called it the best he has ever played against old foe Roger Federer. Serena Williams was just being her dominant self.

The defending champions both made their way back to the Australian Open final, with Djokovic beating Federer 6-1, 6-2, 3-6, 6-3 and Williams defeating Agnieszka Radwanska 6-0, 6-4 on Thursday.

“I’ve had matches where I’ve played similar tennis,” said Djokovic, the top-ranked player in the world. “But I think against Roger, these first two sets have been probably the best two sets I’ve played against him overall throughout my career.”

Hours earlier at Rod Laver Arena, Williams advanced to within one win of another Grand Slam milestone. If the six-time Australian Open champion wins Saturday’s final against seventh-seeded Angelique Kerber, she will equal Steffi Graf’s 22 major singles titles, a record in the Open era and the second-most in history behind Margaret Court’s 24.

“I was able to do everything that I needed to do,” Williams said of Thursday’s match. “I was really hitting just all the right shots, making little to no errors, which is kind of hard to play like that.”

Djokovic, a five-time champion at the Australian Open, advanced to his sixth final at Melbourne Park. He’ll find out who his final opponent will be after Andy Murray takes on Milos Raonic on Friday.

For Federer, the signs were ominous from the beginning. Djokovic held his first service game at love and broke the 17-time Grand Slam champion in the second. After seven minutes, Federer was trailing 3-0.

The first set was over in 22 minutes. Most spectators — including a woman with a sign reading: “Just Married But Willing to Exchange for Federer” — were behind him, applauding Djokovic’s service faults and giving Federer a standing ovation when he broke to go ahead 4-2 in the third set.

The end came quickly in the fourth. Djokovic broke Federer in the eighth game to go up 5-3 — not even a stunning down-the-line shot after he earlier chased down a lob on the same point could save the Swiss great.

Djokovic held three match points in the next game and he clinched it when Federer netted a backhand. Djokovic, who won three Grand Slam titles last year, took a 23-22 edge in his 45 meetings with Federer.

“Definitely I’ve played unbelievable the first two sets but that’s what is necessary against Roger,” Djokovic said.

Asked about the crowd support for Federer, Djokovic displayed Swiss-like diplomacy.

“When I play Roger it’s something that is expected, in a way, considering his career and his greatness on and off the court,” Djokovic said. “He’s loved. He’s appreciated. He’s respected around the world. For me it’s normal in a way.”

Federer said he wasn’t surprised by Djokovic’s early blitz.

“I’ve seen Novak play this well before,” he said. “It’s tough when it’s from the start because obviously you got to try to stop the bleeding at some point. He can get one or two sets all of a sudden … and it’s tough to get back into it.”

In the first semifinal match, Kerber ended Sydney-born British player Johanna Konta’s surprising run with a 7-5, 6-2 win to reach her first Grand Slam final. Konta was the first British woman since 1983 to reach the semifinals at a major tournament.

Williams is the overwhelming favorite in the final, and not just based on recent form. She continued her perfect streak in seven Australian Open semifinals.

“I definitely block it out,” Williams said in reply to a question about equaling Graf’s mark. “I was one off last year, too. If I don’t win on Saturday, I’ll still be one off.”

Despite all her success, it is a loss that is inspiring Williams in this tournament. She was two matches away from a calendar-year Grand Slam in 2015 when she lost to Roberta Vinci in the U.S. Open semifinals.

“Physically I’m feeling a lot better, mentally I needed that break after the Open,” Williams said, but “I didn’t think I would do this well this fast.”