By Neil Johnston- Captain Olga Carmona scored an 89th-minute winner to spark wild scenes of jubilation among their supporters at Eden Park, Auckland.
Sweden – who have now lost back-to-back World Cup semi-finals – had equalised through Rebecka Blomqvist just 93 seconds earlier and it looked like the match would be going to extra time.
A game of few chances had sparked into life when substitute Salma Paralluelo, 19, gave Spain the lead with just 10 minutes remaining.
They will face England or Australia in the final in Sydney on Sunday.
The semi-final between the Lionesses and the co-hosts is live across the BBC on Wednesday (11:00 BST).
Explosive finish after cagey 80 minutes
While Spain’s players celebrated wildly on the pitch at full-time, Sweden’s dropped to the floor as their World Cup dream came to an end.
There was little evidence of what was to come during a tight and cagey opening 80 minutes.
Spain boss Jorge Vilda opted to recall two-time Ballon d’Or winner Alexia Putellas, whose minutes on the pitch have been limited as she returns from a serious knee injury.
And it was Putellas who brought the biggest cheer of the opening half from the sell-out 43,217 crowd when she nutmegged Manchester City’s Filippa Angeldahl.
It took until the 42nd minute for the first shot on target, Sweden’s Fridolina Rolfo denied her third goal of the tournament by her Barcelona team-mate Cata Coll.
Spain dominated possession but Sweden’s defence, which has been solid and resolute for the past month, frustrated their opponents for long periods, while the Swedes once again used a familiar weapon to try and find a breakthrough.
Seven of their 11 goals at this tournament before the semi-final had come from set-pieces but Coll, who had not started a senior game for Spain prior to the World Cup, stood up well to Sweden’s inswinging corners, which had caused havoc in previous matches.
Then came the explosive finish.
Paralluelo, who scored the winner in the quarter-final against the Netherlands, kept her composure to fire Spain ahead before substitute Blomqvist poked home the equaliser.
With extra time looming, Carmona sent Spain through with a shot which went in off the bar following a corner.
Spain recover from squad turmoil
Spain had only won one of their previous seven Women’s World Cup matches before this tournament. They now head for the final after their fifth – and most dramatic – win in New Zealand.
This historic win for Spain came just 15 days after they were beaten 4-0 by Japan in a group match.
Boss Vilda said after that defeat “no-one should lose hope” and his players have responded by eliminating Switzerland, the Netherlands and Sweden.
Spain had come into this tournament under a cloud after 15 players had threatened to quit the team as they were unhappy with Vilda’s methods, and the coach initially exiled them from the squad.
Three of the 15 – Mariona Caldentey, Aitana Bonmati and former Manchester United defender Ona Batlle – were eventually included in his squad for the World Cup.
Spain appear to have put those differences to one side as all three players helped their country reach the final on a memorable night for La Roja.
‘I hope Spain win’
It was the same old story for Sweden as they lost for the fourth time in five World Cup semi-finals, having knocked out 2015 and 2019 winners the United States and Japan in their past two matches.
Their players have been ruthless and efficient at this tournament but looked heartbroken after going so close to forcing extra time.
“There are so many emotions right now,” said boss Peter Gerhardsson. “Everyone just feels sadness and huge disappointment.”
Sweden now go to Brisbane for the third-place play-off on Saturday (09:00 BST).
“We will be really, really ready for that game,” added Gerhardsson, who said he hoped that Spain would go on to win the World Cup.
Sweden’s defeat means Caroline Seger, their long-term captain, will end her international career without a World Cup winners’ medal after five tournaments.
Seger has been limited to just 69 minutes of action at this World Cup because of a calf injury. (BBC Sport)
