By Matt Majendie
French Open champion Schiavone, who had previously won just three matches since her Roland Garros triumph, wrapped up the first set in 29 minutes with a forehand down the line.
The number six seed was even more dominant in the second set as Morita, with only one grand slam singles victory in 10 attempts, proved unable to pose much of a threat.
Schiavone's only scare of the match came with a break point down 3-0 up in that second set but a volley down the line saved the break and she comfortably ended the match in 58 minutes.
The 30-year-old from Milan relied on her serve-and-volley tactics against her opponent in front of a sparse crowd at Flushing Meadows.
Playing under clear blue skies, Schiavone dominated the match, winning 56 points to Morita's 27 in a match littered with errors by both players.
Schiavone, who became the first Italian women to win a grand slam at the French Open in May by defeating Australia's Samantha Stosur, struggled with her first serve in her opening match in New York.
But a first-serve percentage of only 48 percent was not enough to unsettle Schiavone, who now faces the winner of the match between Italy's Maria Elena Camerin and Australia's Sophie Ferguson.
(Editing by Frank Pingue)