Rapinoe’s two strikes, on either side of halftime and another from Christen Press in the 61st minute powered the Americans to the top of Group D after Sweden and Nigeria had earlier battled to a 1-1 draw.
“That was a little bit of shaky game for us, especially the first 30 minutes, Hope (Solo) came up absolutely huge for us, I think she made three saves that I don’t think anyone else in the world can make,” Rapinoe told reporters.
“Three points. That’s what is most important, especially in this group that is shaping up a little weird.”
Having achieved just two draws in their 24 previous meetings against the U.S., Australia came out looking determined to end their frustration when Emily Van Egmond unleashed a thunderbolt from just inside the penalty area that forced a diving save from Hope Solo.
The U.S., however, drew first blood in the 12th minute when Rapinoe’s long range shot deflected off an Australian defender leaving a flat-footed Melissa Barbieri no chance.
The goal did nothing to deflate the Matildas as Australia continued to push forward with Lisa De Vanna celebrating her 100th international appearance with her 36th goal to leave the sides level 1-1 at halftime.
The U.S. broke the deadlock in the 61st minute when Sydney Leroux made a deep run down the wing and fed an unmarked Press in the box before Rapinoe sealed victory in the 78th minute.
“Obviously very disappointed in the result, I felt the performance was quite good for large patches of the game,” said Australian coach Alen Stajcic, whose side meet Nigeria on Friday.
“I thought we had plenty of chances, especially in the first 30 minutes, I guess a couple of bits of class in the end from Rapinoe changed the game.
“There are no easy games in this group and a long way to go.”
No nation will face a tougher road to the final than those in Group D, which features three teams ranked in the top 10, the U.S. (2), Sweden (5), Australia (10) and the top African nation Nigeria (33).
The U.S. will next meet Sweden where they face an intriguing showdown with former coach Pia Sundhage, who had been in charge of the Americans for five years and led them to two Olympic gold medals and a runner-up finish in the 2011 World Cup.
“It’s another opportunity to try and get some points,” said U.S. coach Jill Ellis.
“It’s going to be two teams that know each other very well.”
(Editing by Greg Stutchbury)