MELBOURNE, Australia — Novak Djokovic and Roger Federer are 22-all in career head-to-heads, have nine Australian Open titles between them, and warmed up for a semifinal meeting with clinical quarterfinal wins.

Six-time champion Serena Williams advanced to the semifinals yet again, extending her dominance in a 12-year rivalry with an 18th straight win over Maria Sharapova.

The three most decorated players from Melbourne in the Open era all won in straight sets Tuesday, with Williams starting the roll with a 6-4, 6-1 win over 2008 champion Sharapova in a rematch of last year’s final. Up next for her is fourth-seeded Agnieszka Radwanska, who beat No. 10 Carla Suarez Navarro 6-1, 6-3 to reach a Grand Slam semifinal for the fifth time.

Williams has won every semifinal she’s contested at Melbourne Park, and gone on to win the title each time.

Djokovic’s mark is almost as good — he’s 5-0 in semifinals, and in finals, in the season’s first major. He advanced with a 6-3, 6-2, 6-4 win over No. 7 Kei Nishikori in the night match on Rod Laver.

Four-time champion Federer capped the afternoon session with a 7-6 (4), 6-2, 6-4 win over No. 6 Tomas Berdych, reaching his 12th Australian Open semifinal and his 39th in a Grand Slam. He hasn’t gone past the semifinals here since winning the title in 2010.

Williams’ win over Sharapova was the marquee match of the day, improving her record to 19-2 in a rivalry that goes back to 2004.

She attacked Sharapova’s strength, the serve, and it paid off.

“It was super intense,” Williams said. “She’s an incredibly intense, focused player who was No. 1 and has won so many Grand Slams for a reason. You have to come out with a lot of fire and intensity.”

Sharapova has won five majors, including the 2008 Australian title, and has been in three other finals at Melbourne Park.

In her fourth-round win against No. 12 Belinda Bencic she had a career-high 21 aces. Against Williams, she had three, and seven double-faults. Williams had 13 aces, three double-faults, hit 31 winners to 11, and broke Sharapova’s serve four times.

“She played quite explosive,” Sharapova said. “She was really explosive off the return. Yeah.”

Sharapova broke to open the match and held for a 2-0 lead. But Williams held in the third game and broke to quickly level at 2-2.

Both players struggled with their ball toss at one end, repeatedly practicing their toss to work out the best position to serve into the sun.

Williams also had to concentrate hard to hold in the ninth game, when a baby screamed loudly in the stands as she faced breakpoints.

She was able to protect her own serve, and go on the attack against Sharapova’, taking the high-risk rather than the high-percentage options with her returns.

After winning an intense first set, Williams had medical treatment — later saying it was just for an upset stomach.

She went on a five-game roll in the second to put the result beyond doubt before Sharapova held serve.

Sharapova hasn’t beaten Williams since back-to-back victories in 2004, when she led their rivalry 2-1. Despite more than 11 years in between, Sharapova isn’t giving up hope of breaking that drought.

“It’s motivating because she’s at a different level,” Sharapova said. “She makes you go back to the drawing board, not just for me, but for many other players. She makes you work. That’s inspiring.”

Federer also has some inspiration in his next match against Djokovic. He lost to the Serbian star five of the six times they met in finals in 2015, including Wimbledon and the U.S. Open.

The 34-year-old Federer used a full array of shots, including some vintage backhands, in his 48 winners, to avenge two losses to Berdych at Wimbledon in 2010 and the 2012 U.S. Open.

“Tomas has caused me a lot of problems over the years,” said Federer, who improved to 16-6 against the Czech player. “He’s one of those guys who make you a better player, he’s beaten me on the biggest courts around the world.

He’s now the oldest man since 1979 (Colin Dibley) to reach the Australian Open semis, where he’ll play either five-time champion Novak Djokovic or No. 7 Kei Nishikori.

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