Alcaraz eases into last eight in bid for maiden Melbourne title
The six-time Grand Slam champion won 7-6 (8/6), 6-4, 7-5 to equal his best run in Melbourne and is yet to drop a set.
The Spanish top seed plays home hope and sixth seed Alex de Minaur or 10th seed Alexander Bublik of Kazakhstan for a place in the last four.
If Alcaraz, 22, can break his Australian duck he will become the youngest man in history to win a career Grand Slam of all four majors.
"He started really strong, really strong shots, it was a bit difficult at the start," he said.
"But I knew I would have my chances.
"Overall it has been a really high level of tennis from both sides, really happy I got it in straight sets."
The encounter at Rod Laver Arena took place in significantly cooler conditions compared to Saturday, when temperatures approached 40C and matches on outside courts were suspended.
Alcaraz suffered the worst possible start, his serve broken in the first game by the 19th-seeded Paul.
Alcaraz saw two break points on the American's serve come and go, Paul forging a surprise 3-1 lead.
The Spaniard had Paul under pressure again in the eighth game, Alcaraz this time grasping the chance to break and level the set.
They went to a tiebreak and it was finely poised at 3-3 when a medical emergency in the crowd brought a halt to play for about 15 minutes.
The interruption seemed to hurt Paul more, double-faulting to gift Alcaraz the set.
Alcaraz carried the momentum into the second set, breaking once to move to within a set of victory.
It was just a matter of time after that, Alcaraz sealing an emphatic win in two hours and 44 minutes.
Alcaraz has been especially strong on serve, surprising even himself with how clean he is on his first serve in particular.
"In general in the four matches the serve has been a really important weapon for me," he said.
Alcaraz's new-look serve has been compared to Novak Djokovic and the Serbian great joked in Melbourne that he is expecting a slice of the Spaniard's winnings.
Alcaraz has in the past struggled with precision and a lack of consistency in his serving technique.