- Lauren James (87')
"It's amazing. Anything that's thrown at this team, we show what we're capable of," Kelly told the BBC. "We dig deep as a group and we believe in our ability."
England played with 10 women through extra time after forward Lauren James, their top scorer with three goals in the group stage, was sent off in the 87th minute for an ill-tempered stamp on the back of Michelle Alonzi after the two went down in a tangled heap.
"This team is special, we did it in the Euros, we did it in the Finalissima [a shootout win against Brazil], and we're here again tonight and doing it. And we keep pushing forward. There's more to come from this special team," added Kelly, who scored the winner in the Euro 2022 final against Germany.
On her approach to the decisive penalty, she said: "It's 'I'm going to score.' That's how I look at it. Once I win that mental battle, we're good."
England keeper Mary Earps, named player of the match, said the Finalissima shootout in April was a terrific warmup.
"I don't even practice a shootout, to be honest," Earps said. "It's a very special moment, a very special pressure cooker."
Nigeria forced Earps to work early, and the England keeper stood tall with a couple of great saves in front of 49,461 fans at Lang Park.
Ashleigh Plumptre launched a rocket from 25 yards out that rang off the underside of the crossbar, then moments later forced Earps to make a diving save with a shot from the centre of the box.
England were awarded a penalty when Daly was pushed from behind in the box by Rasheedat Ajibade, but it was overturned after a VAR review.
The Lionesses did not have a shot on target until the 77th minute, when Daly had a terrific chance with a header off Greenwood's corner that forced goalkeeper Chiamaka Nnadozie to get down quickly and save.
England sat back in their own half for most of extra time, and substitute Asisat Oshoala fired a close-range shot minutes before the final whistle that Earps dove to scoop up.
England, making their sixth World Cup appearance, are hoping to top their best finish of third in 2015. They were fourth four years ago in France.
The 40th-ranked Golden Falcons bow out of their ninth World Cup in the round of 16 for the second consecutive time.
- Melissa Borjas