Simone Laudehr finished off a 54th-minute goalmouth scramble with a thunderous volley high into the net to give Germany a 1-0 win over Nigeria and a place in the Women's World Cup quarter-finals on Thursday.

At the other end, goalkeeper Nadine Angerer celebrated her 100th international with a clean sheet which kept the host team perfect with two victories, but hardly convincing in the three-week tournament it is favoured to win.

After France ran up a 4-0 win over Canada to also advance, Germany will have to beat its neighbour next Tuesday if it wants to top Group A. Nigeria was eliminated along with Canada.

"We are happy to advance but we have to work on our game," Germany coach Sylvia Neid said.

With Nigeria needing victory to stay in contention, Germany knew the task ahead. And despite the support of a 48,817 sellout crowd in Frankfurt, it managed little beyond territorial domination.

In a sometimes rough game which referee Cha Sung-mi had trouble controlling, Nigeria went head-to-head with Germany as much as possible but was unable to create many chances against the two-time defending champion.

Germany stuck with the same lineup as the one which beat Canada 2-1 in the opener, keeping veteran star Birgit Prinz in front of her home crowd despite a disappointing opening game.

She was just as poor on Thursday. After a missed overhead kick halfway through the game, she glanced upwards at the sky in exasperation, knowing her poor form of the season has extended into the World Cup. The 33-year-old Prinz is looking for one more goal to become the first woman to score at least once in five World Cups. She leads the all-time list with 14 goals.

It was bitter irony that just after Neid took Prinz off, the match turned.

"I substituted her because I wanted more pressure upfield," Neid said.

Midfielder Celia Okoyino Da Mbabi swung in a low free kick from the left, a first stab for goal was smothered, and a shot from Alexandra Popp was blocked but only as far as Laudehr, who blasted home.

Finally, the German flags went up, the roar of deliverance was deafening, and Germany was on its way to the quarterfinals.

"It didn't go smoothly," Laudehr said.

"We knew that they would be tough because they needed three points. They made our life difficult," she said.

Even though Neid warned of a tough game, the fans eyed the statistics instead. Germany beat Nigeria 8-0 in a friendly this season. And overall, Germany was 6-for-6 with a 21-2 goal differential.

Expectations of an easy game between the No. 2 and No. 27 in the FIFA rankings were proven wrong, as Nigeria kept putting in crunching tackles, was on edge all the time, and not ready to leave the tournament easily.

But tougher opposition is coming up for Germany, with France next.