Swiss Federer, who has been in sizzling form since reaching the Wimbledon finals, swept past Argentina's Leonardo Mayer 6-1 6-2 6-2 in his opening match at the U.S. National Tennis Centre.
"I feel good now," Federer, who is seeking to add to his record 17 grand slam titles, said on Tuesday. "I actually wasn't so confident yesterday and today. I just felt like maybe could be one of those matches I just couldn't see coming.
"Thankfully I took this match extremely serious," said the 34-year-old Swiss, who had fended off five match points in beating Mayer last year in Shanghai
Also in action on Thursday will be third-seeded Scot Andy Murray and fifth seed Stan Wawrinka of Switzerland.
Murray, who advanced into the second round with a four-set win over controversial Australian Nick Kyrgios, faces French left-hander Adrian Mannarino while Wawrinka comes up against South Korean teenager Chung Hyeon.
In the women's championship, second-seeded Romanian Simona Halep plays against Ukrainian Kateryna Bondarenko before fourth seed Caroline Wozniacki of Denmark meets Czech Petra Cetkovska.
Also in action on Thursday will be big-serving Czech Petra Kvitova, the fifth seed, who faces American Nicole Gibbs in a second-round match at Louis Armstrong Stadium.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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