Sharapova, who lifted her fifth Grand Slam title at the French Open this year, fought back from a set down to beat 95th-ranked Romanian Dulgheru 4-6, 6-3, 6-2 yesterday.
The fifth-seeded Russian was reluctant to blame the windy conditions in the cavernous Arthur Ashe Stadium court for her difficulties, which included 46 unforced errors.
And after two hours and 26 minutes on court -- in a match that began in hot sunshine and ended under the floodlights -- -- she had her 17th three-set win of the season, the most on the WTA tour.
"Overall I felt like in the end I was in much better shape than she was and I could have played another few sets. Mentally that helped me a lot."
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Sharapova was one of the day's headliners, along with Australian Open winner Stan Wawrinka and five-time Grand Slam champion Venus Williams on a day that saw two-time defending women's champion Serena Williams along with top men Novak Djokovic, Roger Federer and Andy Murray all having a day off.
Wawrinka, the third seed from Switzerland, faced Brazil's Thomaz Bellucci in one of two men's second-round matches on the slate.
The first-round exits of Steve Johnson and Ryan Harrison yesterday meant just three American men reached the second round, the fewest in US Open history.
John Isner, the 13th-seeded US number one, Sam Querrey and wildcard Tim Smyczek all booked their second-round berths on Tuesday.
American women were keeping the flag flying, and Venus Williams did her part.