Alcaraz said after his third-round win that he was happy with the level of fitness he had shown in the early rounds following his lengthy absence, while he demonstrated against Paul that the quality of his shot-making is as good as ever.
One sensational cross-court forehand winner early in the second set, which landed in from an almost impossible angle, was measured at 103mph.
That came shortly after Alcaraz had broken Paul’s serve in the 10th game of a tight, high-quality opening set to take it 6-4.
Paul, who was attempting to reach the quarter-finals of his home Grand Slam for the first time, battled hard throughout but Alcaraz proved to be too strong.
Paul had two break points when Alcaraz served for the match at 5-4 in the third set, but the two-time US Open champion put together a run of four straight points to seal victory.
Former British number one Tim Henman told Sky Sports: “When you haven’t played tennis for four weeks, it seems a lot and you can be a bit rusty. This is four and a half months.
“If you would have given Alcaraz a blank piece of paper at the beginning of the tournament and asked how he’d want the first four matches to go, he would have scripted it exactly like that.
“He’s had a few slightly challenging moments but, in the important moments, he’s just come up with incredible tennis. That’s got to give him so much confidence moving forward.”
Later on Sunday, home hope Frances Tiafoe delighted American fans with a entertaining victory over 2021 champion Daniil Medvedev.
Tiafoe saved a set point in the third-set tie-break before wrapping up a 7-6 (7-1) 6-4 7-6 (8-6) win moments later to maintain his perfect record on Louis Armstrong Stadium.
The 11th seed has won all 10 of his matches on the US Open’s secondary show court, while it is just his second win in eight appearances against Russian Medvedev.
Tiafoe, a two-time semi-finalist in New York, will face fellow American Alex Michelsen in the last eight after the 22-year-old beat Argentina’s Tomas Martin Etcheverry 7-6 (8-6) 6-4 6-4 to reach his first Grand Slam quarter-final.