England survive Nigeria scare, Australia also into World Cup quarters
European champions England will play either Colombia or Jamaica in the last eight on Saturday, but they got there the hard way.
Chloe Kelly scored the winning penalty in Brisbane as England beat Nigeria 4-2 in the shoot-out after a tense last-16 tie finished 0-0 at the end of extra time.
England had a major scare before a crowd of 49,461, having come through the whole of extra time a player short following the 87th-minute sending-off of James for a stamp on Nigeria's Michelle Alozie.
Coach Sarina Wiegman, who welcomed key midfielder Keira Walsh back into her side after injury, called it "a very, very hard game".
"How we did that and how the team just kept going, I'm so proud of them," said Wiegman, whose side are regarded as favourites to take the crown from beaten holders the United States.
Georgia Stanway put the first penalty of the shoot-out wide for England, but Desire Oparanozie and Alozie followed suit, both missing the target with Nigeria's first two attempts.
Beth England, Rachel Daly and Alex Greenwood all scored for England before Kelly converted the decisive kick.
"It's amazing, anything that's thrown at us we show what we're capable of," said the Manchester City forward Kelly, who scored the winning goal in last year's European Championship final.
"We've been practising (penalties) a lot and it's working."
The defeat was cruel on Nigeria, the world's 40th-ranked team, who followed up their impressive performances in the group stage by pushing England all the way.
Their England-born defender Ashleigh Plumptre crashed a shot off the woodwork in the first half and Uchenna Kanu also hit the frame of the goal.
"We had every opportunity to get the result and unfortunately we didn't get it done," said their American coach, Randy Waldrum.
"I think we could have (won it in 90 minutes). We had the best chances, we hit the crossbar twice in regulation play. We were a bit unlucky not to get something out of it."
England will discover the identity of their quarter-final opponents on Tuesday when Colombia face surprise-package Jamaica in Melbourne.
Kerr makes comeback
World Cup co-hosts Australia are also into the last eight as their skipper Kerr came off the bench in a 2-0 win over Denmark in front of nearly 76,000 fans in Sydney.
They will play France or Morocco on Saturday in Brisbane after making fairly light work of a toothless Denmark.
To cap a good night's work for the Matildas, talismanic striker Kerr came on with 10 minutes left to huge cheers for her first action of the tournament after a calf injury.
The dangerous Caitlin Foord ran Denmark ragged throughout and scored a fine first after being set up by the impressive Mary Fowler on 29 minutes.
Hayley Raso grabbed a second to make the game safe 20 minutes from time.
The Chelsea predator Kerr, who was supposed to have been the face of the World Cup before injury struck on the eve of the tournament, said it was "a big relief to be back".
"I feel good. I think I was a bit rusty, but, no, I feel great.
"I'll sleep better tonight than I have for the last three weeks."
Denmark coach Lars Sondergaard said he was "proud but disappointed", having seen his side have the better of the opening part of the game.
"The match today was decided by Australia's effectiveness in front of goal and us not being so efficient in front of goal," he said.
"I think we started better. Up until the 1-0, I think we were the better team and played a very good game up until then."
The home side are getting up a head of steam at this World Cup, where the demise of the United States has opened the door for a new champion.
"I think we're embracing it, I think the girls are loving it," Kerr said of the growing expectation and excitement.
"The Australian public has been amazing. We've felt the love, just walking down the street it's been a real buzz."