A second-half strike by Rosana earned Brazil a 1-0 victory over Australia in its opening match at the Women's World Cup on Wednesday in Monchengladbach, Germany.

The breakthrough in a hard-fought Group D match came in the 54th minute, when Cristiane capitalized on some scrappy Australian defending to head the ball to the 28-year-old Rosana, who took one touch past a defender before unleashing her shot past the helpless Melissa Barbieri.

"We scored in a very hard match, a well-balanced match, but thank God we scored and we can relax ahead of the rest of the tournament," Brazil coach Kleiton Lima said. "This cup is surrounded by a lot of glamour."

Lisa De Vanna might have grabbed a late equalizer but fired over in the 87th minute with only the goalkeeper to beat, and Australia also went close from a corner at the very end.

In the earlier Group D match, Emilie Haavi scored a late winner to give Norway a 1-0 victory over tournament newcomer Equatorial Guinea.

"We have to improve when you play a World Cup," Lima said. "Despite the fact players are very experienced, they might be nervous, they might be anxious in the first game, but that's now out of the way."

Brazil signalled its intent to attack when it lined up with three in defence, but Australia coped well with the likes of Cristiane and five-time FIFA player of the year Marta.

"Marta is a fantastic player, she's outstanding," her coach said. "But you cannot peg everything on Marta. We play with 11 players. They have to help her and she has to help them — we're a team."

She started brightly, skipping past a number of challenges before putting in a cross in the third minute, and Servet Uzunlar's interception was crucial a minute later with the 25-year-old Brazilian through on goal.

"I was really pleased with the way we defended against Marta," Australia's Scottish coach Tom Sermanni said. "I don't know if she got a shot on goal today."

Rosana was unlucky to see her header land on the roof of the net in the ninth minute, after a flowing move instigated by Marta's delightful chip forward.

The Australians showed they were not intimidated, however, with De Vanna displaying wonderful trickery on the left wing, and Elise Kellond-Knight playing the ball through the legs of a Brazilian before clearing from defence.

They might have scored from a free kick that caused panic in the Brazilian defence before Fabiana finally managed to clear in the 19th, while Andreia was forced to react to stop a good shot from Kyah Simon.

"We've come here to try and play good quality football," Sermanni said.

Brazil looked disjointed in the face of Australia's pressing game, and passes went astray as it was forced to rely on individual efforts from Marta, who drilled a shot narrowly wide in the 35th.

Lima acknowledged his side's difficulties.

"We never got the ball, once we got the ball — when we stole it — we couldn't keep it," he said.

Cristiane should have scored a minute later when she fired over from close range, but Rosana — the player of the game — made no such mistake with her second-half finish.

"I dedicate this goal to my teammates," Rosana said. "There's no point in scoring a goal and conceding too."