The seven-time Grand Slam champion has hit top form in New York after nearly five months out with a right wrist injury and extended his major match-winning streak to 18 with a stunning display of shotmaking against a fellow big-hitter.
Alcaraz's serve came under pressure in the third game when Paul fired an exquisite 160km/h forehand winner around the net that brought Arthur Ashe Stadium to its feet, but the Spaniard stood firm before striking late to snatch the opening set.
The 23-year-old left a vapour trail with a crosscourt winner to carve out an early opening in the second set and swiftly took a 2-0 lead, before trading breaks with Paul and breezing through the remaining games for a commanding lead.
Even with much of the showcourt crowd yearning for a home winner, second seed Alcaraz continued to steal the show with his audacious play and moved to the brink of improving his win-loss record against American players at the Grand Slams to 13-0.
After shifting down to cruise mode, Alcaraz briefly flinched at the finish line but he regrouped to deliver the knockout blow and set up a meeting with American Ben Shelton or Greek Stefanos Tsitsipas in the next round.
"I played my game. I tried to play my style," Alcaraz said in an interview on court after his win.
"Tommy is such a talented player. His shots are pretty dangerous and sometimes it is really difficult to control the ball when it comes to you. I just tried to be ready for a battle and tried to be aggressive all the time.
"I tried not to let him stay [high up] on the court and I think I did pretty well to put so much pressure on return games, which for me helped a lot to play relaxed, to play calm and think clearly. I'm really happy with the performance today."
American Frances Tiafoe outclassed former champion Daniil Medvedev 7-6(1) 6-4 7-6(6) to to book his spot in the last eight.
Tiafoe trailed Medvedev 1-6 in career head-to-head before Sunday (Monday AEST). His only victory had come at the team competition Laver Cup but he cracked the code when it mattered to him the most, repeatedly striking near the net with surgical precision.
"Daniil has been so good, he's beaten me so many times. This is the first time I've beaten him in a regular match," said the 11th seed.
"Everything is feeling really good. I'm coming forward, I'm having fun."
Tiafoe will next play compatriot Alex Michelsen.
