Sam Kerr came off the bench as Australia surged into the Women’s World Cup quarter-finals with a 2-0 win over Denmark in front of nearly 76,000 fans in Sydney on Monday.

To cap a good night’s work for the Matildas, talismanic striker and captain Kerr came on with 10 minutes left to huge cheers for her first action of the tournament after a calf injury.

Earlier in the day, England beat Nigeria on penalties to scrape into the quarter-finals, despite being down a player after Lauren James was sent off in the 87th minute.

The dangerous Caitlin Foord terrorised Denmark throughout and scored a fine first after being set up by Mary Fowler on 29 minutes.

Hayley Raso grabbed a second to make the game safe 20 minutes from time.

Denmark were contesting their first knockout game at the World Cup since 1995 and they had the first sniff of goal, but Rikke Madsen just failed to connect with the ball while sliding in at goal.

The Danes, ranked 13th in the world to Australia’s 10, could have taken the lead on the quarter-hour at Stadium Australia but Pernille Harder shot straight at goalkeeper Mackenzie Arnold.

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.”

The home side are thriving on growing excitement at what they can achieve at this World Cup, where holders the United States are out, opening the door for a new champion.

“I think we’re embracing it, I think the girls are loving it,” Kerr said of the expectation.

“The Australian public has been amazing. We’ve felt the love, just walking down the street it’s been a real buzz.”

Foord was all over the Denmark defence with her pace and movement down the left.

Minutes later she rampaged down the wing again, chopped back inside and let fly with her right foot, the ball taking a big deflection and whistling just beyond the top corner.

Into the second half and Foord seemed to be everywhere, sliding in to stop a Denmark counter-attack and earning vigorous applause from Australia’s coach Tony Gustavsson.

Defender Janni Thomsen decided she had had enough of Foord and was booked for crudely pulling her down as she arrowed towards the Danish box.

The crowd sensed a second could be coming and it duly did, Fowler again playing a key part to set up Emily van Egmond, who teed up Raso to fire into the bottom corner.

Ten-player England survive

Nigeria had the better of the chances, but the European Champions held out for a 0-0 draw after 120 minutes and prevailed 4-2 in the shootout in front of almost 50,000 spectators in Brisbane.

James, the two-goal hero in the 6-1 win against China, received a red card for violent conduct after a needless stamp on Michelle Alozie on 87 minutes.

She will be suspended when the Lionesses face Colombia or Jamaica on Saturday for a place in the semi-finals as they aim to add the World Cup to their European crown.

Nigeria manager Randy Waldrum said his side had shown their inexperience after James went off.

“We created more chances against 11 players than we did against 10,” Waldrum said.

“It goes down to experience, I don’t think our players handled it very well.

“But credit to England, they were very well organised and prepared for it.”

England got off to a terrible start in the penalty shootout when Georgia Stanway fired wide, but Desire Oparanozie could not take advantage and missed in identical fashion.

Beth England made no mistake, but Alozie ballooned her effort high over the bar to give England an advantage they never surrendered, sealing victory when Chloe Kelly – who scored the winner in the final of the European Championship a year ago – calmly converted.

England coach Sarina Wiegman said her team had practised and were prepared for the shootout.

“We have trained for penalties, we had a plan worked out,” she said.

“But at the end it’s the players who make the decisions as to who wants to take the penalties.

“We know how to do it, and we have the experience.”