With his first serve firing on all cylinders and his forehand in blistering form, world No. 12 Paul was blown away in front of a packed night session crowd, with Alcaraz admitting his brilliance ensured they had a brief night out watching the defending champion hit top gear.
"I'm sorry you wanted to watch more tennis. I had to do my work," Alcaraz told the Court Philippe-Chatrier crowd afterwards.
"I could close my eyes and everything went in. My feeling today was unbelievable. I was trying hit every shot at 100 per-cent. I was not thinking about anything else, just hitting forward and yeah, today was one of those matches that everything went in.
"I'm just pleased with everything. We are in a quarterfinal of a Grand Slam at Roland-Garros and this kind of match is never easy.
"I played against Tommy many, many times and every match was really, really difficult. He has beat me twice, so that helped me at the beginning of the match just to focus on my tennis.
"I tried to step on the court and really focus on my things, trying not to go down or let him get into the match again. I was trying to be focused during the whole match."
Tommy Paul didn't try to hide his disappointment, as he was handed one of his heaviest defeats in recent months.
"Not particularly fun," Paul told reporters. "He played some great tennis, returned very well, had me on my back foot all the time, playing so fast.
"Even on the changeovers he was getting up so fast with 20 seconds left. I thought I have got to slow down. He played some amazing tennis.
"He was on offence and that was not what I needed tonight. I did the best I could.
"Everyone bought tickets for the night session so I thought I try my best. Obviously, I did not want it to go like that."
This was a sparkling display from Alcaraz and matches those served up by his great rival Jannik Sinner in the opening rounds of this year's French Open.
Alcaraz and Sinner are by far the best two players in the tournament so far, with former world No 1 Mats Wilander expecting the pair to meet in the final on Sunday.