Marta, a 33-year-old forward, missed Sunday's match with a left thigh injury she suffered last month in training.
The loss could have been worse for the Reggae Girlz, but goalkeeper Sydney Schneider stopped Andressa's penalty kick in the 38th minute.
Four-time Copa America winners Brazil made light work of Jamaica thanks to Cristiane's hat-trick, as the 34-year-old overtook Cristiano Ronaldo as the oldest player to score three goals in a game at any World Cup.
Schneider, a 19-year-old American-born goalkeeper studying at the University of North Carolina, was handed her place after coaches learned she had Jamaican grandparents on her mother's side.
The win puts Italy in a great position to qualify from Group C.
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They play their first game today at 15.30 local time, when they have the intimidating prospect of facing the experienced Brazilian team on the pitch.
Now Formiga has taken Rampone's record as the competition's oldest ever player, her sights are set on taking USA's title as World Cup holders - with Brazil looking to become the fifth nation to win the competition.
"It's so wonderful. I hope we can qualify for the knockout stage because these two goals are meant to help us do just that". Their first game is against Brazil and while they are probably going to taste defeat, they could make things ungainly for their adversaries.
The Aussies quickly picked up the pace and were soon in front through their star Kerr, who was clumsily brought down by the otherwise excellent Sara Gama in the 21st minute.
After that the well-organised Italians slowly squeezed the life out of their opponents.