While Paul owned two early wins from seven previous encounters, he knew better than to hope the top seed’s concentration would waver.
Having fallen in their two Grand Slam showdowns he knew it was a steep hill to climb if he fell behind two sets, so he made a bold attempt to mix it up with an injection of more pace.
Maintaining control in prolonged rallies was another matter and after being broken early he was unable to recover the deficit.
With a two-set lead after an hour and 46 minutes, the wind was in the Spaniard’s sails. It would have been easy for Paul’s level to fade.
Instead, he found his best in a tightly contested third set and hung tough until 5-all before a string of loose errors cost him his serve and ultimately the contest.
Alcaraz marched on to a last-eight clash against sixth-seeded Australian Alex de Minaur or 10th-seeded Kazakhstani Alexander Bublik.
There will be plenty to more to recap in the family chat should he reach a maiden Australian Open semifinal. Distractions, on court at least, will be kept to a minimum.
“Something that I was working on is to maintain the focus in the whole match, which I did today, playing such great tennis since the beginning until the end of the match,” he said.
“So for me it was really, really important more than saving energy, because I just have plenty of (energy). It’s more about how I have been playing during almost three hours, which was really high.”