Teenage winger Salma Paralluelo came off the bench to score a 111th-minute winner for Spain at the Wellington Regional Stadium to reach the FIFA Women's World Cup semi-finals for the first time.

It looked like Mariona Caldentey had sealed the victory in normal time of this quarter-final tie when she hit home an 80th-minute penalty via the post after The Netherlands' Stefanie van der Gragt handled in the box.

Van der Gragt redeemed herself by smashing home a stoppage-time equaliser only for Barcelona’s Paralluelo to find space in the area in extra-time to put Spain back ahead in front of a crowd of 32,021.

"It means everything for me, it was a unique moment, great euphoria... I'm extremely happy," 19-year-old Paralluelo said.

Spain were the deserved winners after dominating the match for lengthy periods against a side who were beaten in the final in Paris four years ago by the United States.

But the Dutch were left feeling aggrieved by a controversial video assistant referee (VAR) decision in the second-half as referee Stephanie Frappart initially gave a penalty for Irene Paredes knocking Lineth Beerensteyn to the ground, only to overturn her decision.

VAR then stepped in to give Spain a penalty for Van der Gragt's handball.

"VAR did not do its work properly, but Spain deserved to win," said Dutch coach Andries Jonker.

Spain also had a goal disallowed in the 37th minute when Esther Gonzalez put the ball in from close range after Alba Redondo miscued her volley into the striker's path, but it was ruled out for offside following a review.

Spain's coach Jorge Vilda did not care in the end.

"The goal from Salma, it was sheer joy," he said.

"Salma is a player with enormous potential and she's not reached her best yet. 

She's a very young player who has been training one year in football specifically, and the best of Salma we'll see it in the future. 

"Now she's excellent, but in the future it's going to be much, much more."

The defeat of Japan at Eden Park in Auckland in front of a crowd of 43,217 ensured there will be a new name on the World Cup trophy when the winners are crowned on August 20 as they were the last of the previous winners left in the competition.

Germany and China had both been eliminated in the group stages, while Norway and United States had been knocked out in the previous round by Japan and Sweden, respectively. 

Many experts had tipped Japan to regain the trophy following some impressive early performances.

But Sweden are proving formidable opposition as they reached the semi-finals for the third time in four tournaments.

Defender Amanda Ilestedt gave Sweden a first-half lead just past the half-hour mark with her fourth goal in five games.

This matched the total of France's Wendie Renard to become the top-scoring defender at a single Women's World Cup.

VAR also played a vital role in this game when it awarded Sweden a penalty in the 50th minute for handball against Fuka Nagano.

Manchester City's Filippa Angeldal converted the spot-kick to give them a cushion.

In the 76th minute, Japan were awarded their own penalty, but Riko Ueki hit the crossbar with her attempt.

Honoka Hayashi did pull a goal back three minutes from the end, but Sweden saw the match out comfortably, a testament to their tactics which ensured Japan were never able to settle properly throughout the game.

"We were talking about being close to them and keeping on pressure," Sweden's forward Sofia Jakobsson said afterward. 

"If we couldn't win the first ball, going in for the second, and I think that worked really well in the first until we scored the second goal. 

"Japan was growing and they put pressure on us, but I'm super proud of how the team played."

Sweden are now set to take on Spain in the first semi-final of the tournament at Eden Park on Tuesday (August 15).

The remaining two quarter-finals are due to take place in Australia tomorrow.

The first one is scheduled to see England meet Colombia at Stadium Australia in Sydney.

That is due to be followed at Lang Park in Brisbane when hosts Australia play France.