The Belarusian fifth seed, the highest-ranked player left in the draw, will play another unseeded player, Poland's Magda Linette, for a place in Saturday's final.

"It feels really special to be in the semi-finals here, it was a tough match," said Sabalenka, competing in her first Australian Open quarter-final.

"I'm super happy with the win and it was so great to play here today, the atmosphere was unbelievable."

Sabalenka came into the match as many observers' favourite for a first major. She won the recent WTA Adelaide International and had not dropped a set in 2023 in eight matches.

The world number five had reached the US Open semi-finals in each of the last two seasons and made the final four at Wimbledon in 2021. 

By contrast, 64th-ranked Croatian Vekic, aged 26, has been working her way back to the top 20 after knee surgery two years ago that she thought might end her career. 

It was only her second major quarter-final after the 2019 US Open. 

But Vekic had won five of the pair's six meetings, including at the Tokyo Olympics and in San Diego last October,  and she was able to put fierce pressure on Sabalenka's serve early on.

The Belarusian withstood the onslaught, saving three break points to lead 2-1.

She broke Vekic to love for 3-1 but the Croatian got straight back on serve in the next game, securing it on the first of two more break points.

Vekic's serve remained shaky and she had to save break points in each of her service games, not helped by seven double faults in her first three service games.

Vekic tried to mix up her play, delicate drop shots and punishing forehand winners creating more openings on Sabalenka's serve.

But this version of Sabalenka, who has so often been unhinged by nerves in the past, refused to buckle and edged ahead again before taking a decisive break to lead 5-3.

Vekic still had a chance to level as Sabalenka served for the set. But she went just wide with an attempted forehand winner and Sabalenka prevailed 6-3 after a titanic 60-minute battle.

"I think just because I was calm and I kind of expect this game from her," said Sabalenka, 24.

"So I was able to stay in the game no matter what. So I think this was the key."

Sabalenka had the momentum and put the Vekic serve under more pressure at the start of the second set, stretching out to a double break for 3-0 as the Croat's double fault count soared to 12.

Sabalenka wobbled, serving two double faults and facing break points, as she had done on every service game, when serving for the match at 5-2.

After three deuces and with the tension rising, Sabalenka got over the line on her first match point.