Second-half goals from Osinachi Ohale and Asisat Oshoala gave Nigeria a stunning 3-2 win over Australia at the Women's World Cup on Thursday to leave the co-hosts in danger of an early exit.

In front of 49,156 fans in Brisbane the Matildas missed a golden chance to reach the last 16 and instead now face a must-win final group game against Olympic champions Canada.

In contrast, Nigeria top Group B and play Ireland -- who are already out of contention -- with the knockout rounds in sight.

"We've talked about believing in each other and that the success is going to be in the unity of the team," said Nigeria's coach Randy Waldrum, whose team held Canada 0-0 in their first game.

"To think we got two results against two top teams says a lot about our heart and the competitive desire that the team has.

"It's not always the best talent that wins, it's the team that works best together."

Australia captain Steph Catley felt that her side -- who actually took the lead and dominated in the first half -- had enough chances to win the game.

But she conceded: "They were great on the counter and they finished their chances.

"A lot of things (went wrong). We weren't patient enough at times and we weren't clinical enough," she told Optus Sport.

"We had a lot of set-pieces tonight that usually maybe one or two go in.

"We've just got to move on as quick as possible because this is what World Cups are about.

"Our backs are up against the wall now, and it's not how we would have liked it, but nothing good comes easy."

- Defensive mix-up -

A Nigeria win seemed improbable after a first period which Australia dominated, although they struggled to break down the Super Falcons' defence.

Nigeria frustrated Canada in their stalemate and did the same to the Matildas, who lacked the penetration that the injured duo of Sam Kerr and Mary Fowler would have given them.

Australia finally got reward in the first minute of stoppage time when a poor goal kick from Nigerian keeper Chiamaka Nnadozie was picked off and Caitlin Foord's low cross was met by Emily van Egmond, who calmly slotted the ball into the net.

But any hopes of taking a 1-0 lead into the break were dashed in the last play of the half.

Rasheedat Ajibade cut inside and her shot deflected into the path of Uchenna Kanu, who beat Australian goalkeeper Mackenzie Arnold with a prodded finish at the back post.

Defender Ohale popped up to put Nigeria in front in the 65th minute when she headed home after Arnold could only parry a shot into her path.

Barcelona's Oshoala, who came on in the second half, then took advantage of a mix-up between Arnold and defender Alanna Kennedy to get between them and fire home from an acute angle.

Australia got one back through Kennedy in the 10th minute of stoppage time but the Nigerians held on for a famous victory.

The 66-year-old American Waldrum afterwards said teams like his needed more funding if they are to continue to compete at the top level.

"Not all the teams have collective bargaining like they do here in Australia," he said.

"The sky's the limit if there is investment, and not just in Nigeria.

"There's a lot of countries, not just in Africa, that need more funding."