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 a hat-trick in the 5–0 win against Chinese Taipei.
Morace is probably best known in Italy for having been the first woman to coach a professional men's football team, Viterbese of Italian Serie C1, a post she took in June 1999. She eventually resigned from her position after only two matches, because of heavy media pressures.
Until June 2005, she was head coach for Italy's national women's team. In February 2009 she was announced as the new head coach of the Canadian national women's team. Under her guidance, Canada won the 2010 CONCACAF Women's championship and earned a last place finishing at the 2011 FIFA Women's World Cup having lost all of their games and only scoring one goal. She formally announced her resignation as the coach of the Canadian national women's team on Friday 22 July 2011.