Zverev, who had been taken to five sets in his opening two matches of the tournament, raced past 21st seed Darderi 6-2, 6-2, 7-6 (3) in two hours and 30 minutes on the Arthur Ashe Stadium court.
The brisk victory came as a welcome change for Zverev, whose marathon first- and second-round matches had finished in the early hours of the morning.
"I don't know what to do with myself because it's before midnight," Zverev quipped afterwards.
"I might go back to the practice court, I might go to a bar - that was a joke, unfortunately.
"Compared to the first two matches, the level has been going up."
The 29-year-old French Open champion was in complete control throughout, punishing Darderi's woeful service game to grab an early double break in the first set for a 3-0 lead.
Darderi, who has failed to go further than the fourth round at any Grand Slam in his career, never looked like forcing his way back into the set thereafter.
Zverev mopped up the first set easily and was soon back on the attack in the second, once again securing a quick double-break for a 3-0 lead before holding with ease to go two sets up.
Darderi did manage to rally in the third set, suddenly finding his range with some blistering forehands and holding off four break points in the 11th game to help set up a tie-break.
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But Zverev's superior service game meant there was only going to be one winner in the tie-break, a thunderous serve giving him a 5-2 lead before a scorching forehand into the corner took him to match point.
Zverev then wrapped up victory with his 13th ace of the match.
"I thought my level was very consistent," Zverev said.
"It was just that he started playing incredibly well in the third set. I barely saw anyone hit the ball as hard consistently as he did in the third set," added the German, who will now face Dutch veteran Botic van de Zandschulp in the quarter-finals.