The Swiss, looking to claim a record-extending 20th grand slam title, needed to play five sets to advance into round two as questions were raised over his fitness after a back injury.
He is third up on Arthur Ashe Stadium, where Ukrainian fourth seed Elina Svitolina gets things started against Russia's Evgeniya Rodina.
World number one Rafa Nadal takes on Japan's Taro Daniel last on Ashe, where top-ranked Karolina Pliskova faces home hope Nicole Gibbs.
Two outside bets, Bulgarian Grigor Dimitrov and Austrian Dominic Thiem, are on Louis Armstrong against Russian Andrey Rublev and American Taylor Fritz.
After rain washed out most the play on Tuesday, it is expected to be a sunny day at Flushing Meadows.
(Reporting by Julien Pretot; Editing by Alison Williams)
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