Sam Kerr was one of two Australian players to miss her penalty as Norway beat the Matildas 4-1 in a shootout following an engrossing 1-1 draw on Saturday to reach the quarter-finals of the FIFA Women's World Cup.

Ingrid Engen converted the decisive spot-kick for the Norwegians after both Kerr and Emily Gielnik had failed to convert for the Australians in Nice.

Norway had earlier taken the lead through Isabell Herlovsen before being pegged back by Elise Kellond-Knight late on and taken into extra time.

They could not find a winner in the extra half-hour, despite Australia having Alanna Kennedy sent off, but the 1995 world champions had the last laugh and will go through to a quarter-final against either England or Cameroon.

It is a painful end to Australia's hopes of at least making the last eight, as they had done at each of the last three World Cups.

However, Norway remain on course to meet their stated objective of finishing among the medals despite coming to the tournament without their biggest star, Ballon d'Or winner Ada Hegerberg.

They had drawn first blood, taking the lead just after the half-hour mark. Australia defender Steph Catley failed to cut out Karina Saevik's ball in from the right flank and Herlovsen pounced to score with a clinical finish.

For a long time it looked as though that would be the only goal of the game, with the Matildas left frustrated just before half-time when they were awarded a penalty only for the decision to be overturned.

German referee Riem Hussein pointed to the spot when she saw what appeared to be handball by Norwegian defender Maria Thorisdottir. However, she changed her mind after a review of the replayed images showed that the ball had in fact struck her shoulder.

Kerr and Hayley Raso had already come close for Australia before that and Kerr was denied again early in the second half when she had the ball in the net only to be flagged offside.

Nevertheless, with just seven minutes of normal time left, Ante Milicic's side drew level in fortuitous fashion as Kellond-Knight curled in a low corner from the right and the ball evaded everyone on its way into the net.

Into extra time they went, and Australia were reduced to 10 players in the 104th minute when Kennedy saw the first straight red card of the World Cup for pulling down Lisa-Marie Utland as the substitute ran towards goal.

Vilde Boe Risa hit the bar with an audacious attempt from range just after that, but Australia held on for penalties, only to see Kerr blaze her kick over before Gielnik's was saved while Norway converted all of their efforts from 12 yards.

Earlier in the day, Germany maintained their perfect women's World Cup record by reaching the last eight with another solid performance in a 3-0 win over Nigeria.

The two-time world champions had VAR to thank for their first two goals in a physical encounter in Grenoble, before striker Schueller sealed the win eight minutes from time.

Martina Voss-Tecklenburg's side are yet to concede a goal in their four games at the World Cup so far.

Captain Alexandra Popp gave Germany the lead on 20 minutes, nodding Lina Magull's in-swinging corner inside the far post.

Magull was involved again as Germany doubled the lead minutes later.

The midfielder was caught on the knee as Nigerian left-back Evelyn Nwabouku attempted to clear a loose ball in the area.

After reviewing the incident on the touchline, the referee awarded Germany a penalty, and striker Sara Daebritz made no mistake from 12 yards.

Three yellow cards were awarded in the second half as the Nigerians were unable to battle their way back into the game.

Schueller put paid to their hopes on 82 minutes, pouncing on a mistake from Halimat Ayinde and smashing the ball into the bottom corner.

Germany will face either Sweden or Canada, who play on Monday, in the quarter-final next weekend.