Melbourne, Australia — After backhanding the ball into the crowd when Carlos Alcaraz sent his service return too long, Alexander Zverev screamed. He shook both arms in a victory celebration and again he screamed, a mix of triumph and relief.

Any self-doubt that he could contend for major titles again were expunged in a 6-1, 6-3, 6-7 (2), 6-4 quarterfinal win on Wednesday over the brightest rising star in tennis, earning Zverev a spot in the Australian Open semifinals against Daniil Medvedev.

He'd missed a chance to serve it out in straight sets but didn't waste his second opportunity.

A serious ankle injury at the 2022 French Open and the ensuing layoff made him wonder if he really was good enough to win a Grand Slam title.

A pending trial in a German court over an assault allegation dating back to 2020 has had critics questioning his status on the tour. He has denied the accusations and declined comment on the judicial proceedings scheduled for May.

Alcaraz won Wimbledon last year and was the only player to beat 10-time Australian Open winner Novak Djokovic in a Grand Slam match in 2023.

Zverev went through Alcaraz's credentials as he digested Wednesday's win: No. 1 or No. 2 in the world, two major titles, etc, etc.

“Look, I’m playing one of the best players in the world," Zverev said. "Then when you start winning, obviously your brain starts going. It’s not always helpful but I’m happy I got it at the end."

Speaking in a news conference at almost 3 a.m. local time, Zverev considered the win over Alcaraz as his most important since the ankle surgery.

“I was on top of my game before the injury happened,” he said. “I’m extremely happy to be back where I am and winning these kind of matches, giving myself the chance again. Because last year ... I wasn’t a Slam contender.”

Alcaraz missed the 2023 Australian Open with injury and was into the quarterfinals here for the first time, completing a Grand Slam set.

He had dropped only one set and spent five fewer hours on court than Zverev in the four previous rounds.

“I’m sad with my level today, because I have been playing good tennis,” Alcaraz said. “Obviously quarterfinal of a Grand Slam is a good run. It’s not what I’m looking for, but is not bad.”

Medvedev, a two-time finalist in Australia, outlasted ninth-seeded Hubert Hurkacz 7-6 (4), 2-6, 6-3, 5-7, 6-4 to make it to the semifinals here for the third time in four years.

“I’m so destroyed right now,” No. 3-ranked Medvedev, the 2021 U.S. Open winner, said of his tough run in Melbourne that included a nearly 4 1/2-hour, five-set second-round win that finished at 3:39 a.m.

In the other semifinal Djokovic, on a 33-match winning streak at the Australian Open, will play Jannik Sinner, who beat him twice in three matches at the end of last year.

Zverev was on top of Alcaraz early, winning all but two points on serve in a 29-minute first set. Two service breaks in the second gave the Olympic gold medalist a surprisingly comfortable lead.

Just after midnight, Zverev was serving for a straight sets win at 5-3 when Alcaraz broke for the first time. Alcaraz got back to 5-5 when he chased a shot into the doubles alley and knocked a backhand down the line, beaming a big smile and shaking his racket in a gesture that suggested: “Hello, still here.”

He won the last seven points of the tiebreaker to make it 2-1.

But after an exchange of service breaks to open the fourth and some energy-sapping rallies that had both players sprinting side-to-side to make incredible shots, Zverev got another chance to close out after breaking in the ninth game.

He clinched it about 1:20 a.m. local time.

The women’s semifinal lineup was completed when No. 12 Zheng Qinwen won 10 of the last 11 games to fend off Anna Kalinskaya 6-7 (4), 6-3, 6-1 on Wednesday and Dayana Yastremska beat Linda Noskova 6-3, 6-4.

Defending champion Aryna Sabalenka and U.S. Open winner Coco Gauff will meet in the other semifinal.

Zheng, a U.S. Open quarterfinalist last year, regained control after Kalinskaya won six of the last seven points to take the first in a tiebreaker.

“Really excited. First time for me,” Zheng said. “Of course I’m proud of myself. But this is just the beginning — I still need to play tomorrow."

No. 93-ranked Yastremska won three matches in the qualifying tournament and became only the second qualifier to reach the women’s singles semis in Australia in the Open era.

“It’s nice to make history because at that time I was not born,” she said. “I’m super happy (but) very tired.”

Noskova beat top-ranked Iga Swiatek on her way to her first Slam quarterfinal but struggled against Yastremska.

After the match, Yastremska wrote a message on a TV camera lens and later explained it was “about the Ukrainian fighters, that I’m very proud of them. They really deserve a huge respect.”

She said she’s inspired by representing her country, which has been at war for nearly two years since the Russian invasion.

“It’s my mission here,” she said. “If I do well, I can get — tough to express. I’m just trying to give the signal to Ukraine that I’m really proud of it.”