• American victorious with 5-7, 6-1, 7-6 (8) win
• Advances to her second grand slam final

As Madison Keys stared down a match point in the final set of one of the most extraordinary matches of her career, she had ample reason to slump her shoulders and lament the crushing defeat that seemed to be imminent.

From a set down, Keys had rallied brilliantly, dragging herself back into contention with some of the most destructive, daring ­shotmaking exhibited all tournament. In the breathless final set that followed, when she was so often close to ­losing, the 19th seed continually found the courage and heart to force her way back into the match.

Clashes between players and spectators at Australian Open are just another example of the shouty polarities of our age

Eva Asderaki-Moore probably loves her job. But there were times, during Novak Djokovic’s Australian Open win over Carlos Alcaraz on Tuesday, when the chair umpire clearly had it with the crowd. “Ladies and gentlemen, please,” she pleaded. And then “That’s e-nough!” – which she enunciated like a schoolteacher marshalling her charges on a very long, very noisy coach trip.

You had to feel for her. What is tennis thinking after all? It throws 15,000 people into an arena, whips them up into a state of delirium with some of the greatest feats of athleticism seen in a grand slam quarter-final, then expects pin-drop silence between points. At 1am? When some of these people have been drinking since lunchtime?

• Aryna Sabalenka beats Paula Badosa to reach the final
• Get in touch! Email Daniel Harris with your thoughts

Sabalenka 0-1 Badosa* (denotes server) A big service-winner down the T makes 15-all, but Sabalenka takes control of the next point with a booming forehand return, cleaning up with with another down the line Then, facing a second serve, she steps in a little and starts thwacking … but just when15-40 seems a matter of time, a backhand on the stretch and on to the line hauls Badosa back into the point and eventually the error comes; 30-all. But a double presents break point; another service-winner confiscates it, and so far, the underdog is coping with the pressure well, as I type spanking an ace down the T for advantage. And though she oughtn’t win the next rally, Sabalenka in at the net and unable to finish, she makes her opponent play enough balls such that the error comes. Badosa is into this!

Badosa to serve and ready … play.

The 37-year-old showed killer instinct against younger rival, a willingness to go to hell and back in pursuit of glory

In the most recent late-night exhibition of his insatiable resilience and desire, as he again belied his ageing body to deliver another legendary performance, one of the most significant moments of Novak Djokovic’s quarter-final defeat of Carlos Alcaraz at the Australian Open came as the Serb clung on desperately to his frail momentum.

With a set point on his serve at 5-3 in the third set, Djokovic was hurled around the court by Alcaraz, chasing down a drop shot before stumbling back to the baseline in pursuit of a lob. The frantic point – and set – ended with Djokovic slipping an angled backhand passing shot by Alcaraz before cupping his hands to his ear while the Rod Laver Arena erupted.