Born in Venice, Morace debuted for the Italian women's national team in 1978, against Yugoslavia, at the age of 14. During her career, she made 153 appearances for Italy, scoring 105 goals. While playing in the Italian national women's league, she scored more than 550 goals. She took part in six European Championships as well as the inaugural FIFA Women's World Cup China 1991, where she scored four goals, including recording the first ever hat-trick to be scored at a World Cup in their 5–0 win against Chinese Taipei.