|US Open 2019|
|Venue: Flushing Meadows, New York Dates: 26 Aug – 8 Sep|
|Coverage: Live text and BBC Radio 5 Live Sports Extra commentary on selected matches on the BBC Sport website and app. Click here for Live Guide.|
The German, who has yet to advance past the third round at Flushing Meadows, fired down 21 aces but made 52 unforced errors in a match where the momentum swung from one player to the other.
Zverev said: “If it goes the distance. then I’m ready.
“I’d like easier matches though.”
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The 22-year-old, who beat Radu Albot in the first round, added: “Frances gave me an unbelievable fight today.”
Zverev will play Slovenian Aljaz Bedene, who beat 29th seed Benoit Paire, in the third round.
Elsewhere, in-form Cincinnati Masters champion Daniil Medvedev recorded his 16th win from the past 18 matches with a 6-3 7-5 5-7 6-3 win over Hugo Dellien of Bolivia. The Russian fifth seed will now play Spain’s Feliciano Lopez.
American Denis Kudla’s reward for defeating 29th seed Dusan Lajovic 7-5 7-5 0-6 6-3 is a third-round contest against defending champion and world number one Novak Djokovic.
Belgian 15th seed David Goffin, beaten by Medvedev in the recent final at Cincinnati, defeated Gregoire Barrere 6-2 6-2 6-2 and will play Spain’s Pablo Carreno Busta in the third round.