The 21-year-old German won all of his five break points and thumped 10 aces and 18 winners to dispatch his French opponent in one hour and 49 minutes.
Zverev told reporters he was pleased with his performance, having never reached the third round at Flushing Meadows.
"This was always the Grand Slam where I didn't play my best ever," Zverev said. "Game-wise, I never felt comfortable here. Finally I do."
He added that he was working to minimise distractions to help him focus more on the matches ahead.
"I don't go out at all... I spend the least possible time here on site because that takes energy away," Zverev said. "(I)may be enjoying New York a little less, but that gives me, you know, the credibility to play better."
The up-and-coming Zverev has had a relatively easy road at Flushing Meadows after beating another lucky loser, Peter Polansky, in straight sets in the first round.
He will expect his good fortune to continue when he meets unseeded countryman Philipp Kohlschreiber in the third round on Saturday, having won their last two meetings.
(Reporting by Amy Tennery; Editing by Ken Ferris)
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