MELBOURNE, Australia — Novak Djokovic refused to let anything stop his pursuit of a record 25th Grand Slam trophy in the Australian Open quarterfinals. Not a problem with his left leg. Not an early deficit. And not the kid across the net, Carlos Alcaraz, who was making things difficult and eyeing his own bit of history.

Djokovic overcame it all, just as he has so often along the way to so many triumphs, moving into the semifinals at Melbourne Park for the 12th time with a 4-6, 6-4, 6-3, 6-4 victory over Alcaraz in a scintillating showdown Tuesday night between a pair of stars born 16 years apart and at opposite ends of their careers.

“I just wish that this match today was the final,” Djokovic said. “One of the most epic matches I’ve played on this court. On any court.”

The action was non-stop, the shot-making brilliant, even as the encounter stretched on for more than 3 1/2 hours and nearly to 1 a.m. — never more so, perhaps, than when Alcaraz saved a break point in the fourth set. The 33-stroke exchange was the longest of the evening, and when it ended with Djokovic sailing a forehand long, the capacity crowd at Rod Laver Arena went wild. Djokovic reached for his bothersome leg and yelled toward his entourage; Alcaraz, his chest heaving, leaned on a towel box and grinned.

Turned out that only delayed the final result.

With his wife, son and daughter cheering in the stands — Dad joked about the late hour afterward — the No. 7-seeded Djokovic prevailed thanks to the sort of remarkable returning and no-mistakes-made groundstrokes against Alcaraz that Big Three rivals Roger Federer and Rafael Nadal dealt with for years.

“I felt like I was controlling the match, and I let him get into the match again,” Alcaraz said. “When Novak is at this level, it’s really difficult.”

Djokovic enjoyed some of his own best efforts in the latter stages, pointing to his ear or blowing kisses or spreading his arms while puffing out his chest. There was the forehand winner on a 22-stroke point that earned the break for a 5-3 lead in the third set. There was that set’s last point, which included a back-to-the-net sprint to chase down a lob. Alcaraz wasn’t shy, either, shouting “Vamos!” and pumping his fists after one particularly booming forehand in the fourth set.

When the match ended, Djokovic yelled toward his team’s box, before giving his coach, Andy Murray, a hug. Then Djokovic applauded for No. 3 seed Alcaraz as he left the court.

In women’s play, Madison Keys returned to the Australian Open semifinals for a third time after her 3-6, 6-3, 6-4 win over Elina Svitolina of Ukraine.

The 29-year-old Keys is on a 10-match winning streak after warming up for the year’s first major with a title at Adelaide, where she beat fellow American Jessica Pegula in the final.

Her run to the semifinals at Melbourne Park has included victories over two former Australian Open finalists — Danielle Collins and Elina Rybakina — in the third and fourth rounds.

Keys, the 2017 U.S. Open runner-up, next faces five-time Grand Slam singles champion Iga Swiatek, who swept to a 6-1, 6-2 victory over No. 8 Emma Navarro.