Wearing the captain's armband, Carmona's 90th-minute strike from the edge of the area pinged off the crossbar and into the net two minutes after Rebecka Blomqvist had levelled the match for Sweden in front of a baying crowd of 43,217 at Eden Park.
Salma Paralluelo, the quarter-final hero against the Netherlands, put Spain in the lead with the opening goal in the 81st minute, breathing life into what had been a slow-burning, cagey affair.
Less than a year after a player revolt tore the squad apart, 'La Roja' will have the chance to lift the trophy on Sunday when they face co-hosts Australia or England in the decider.
Sweden bow out after another defeat at the penultimate hurdle, having made the semi-finals in France four years ago and also the last four at last year's European Championship.
In a match-up of Iberian attacking flair and Swedish defensive resilience, Spain were the livelier side early but had little to show for their possession and vigour.
Full back Carmona blazed just wide with a low, long-range effort in the 14th minute and midfield dynamo Aitana Bonmati thrashed a wild shot by the same right post from the edge of the area.
Sweden barely wavered in defence, though, and finished the half ascendant with a typical salvo of set-piece pressure.
A few minutes from the break, Spain were dealt a fright as Nathalie Bjorn chested the ball down and crossed to an unmarked Fridolina Rolfo in the area.
But the Sweden winger's volley was well covered by keeper Cata Coll.
Sweden kept up the heat and Jorge Vilda went to his bench early, replacing Alexia Putellas with Paralluelo, who had scored the winner against the Dutch in the quarter-final.
Paralluelo almost helped break the deadlock in the 70th minute when she kept the ball alive with a cut-back pass to Alba Redondo in close.
Slumped on the turf, Redondo swung a leg out but could only put her shot into the side netting.
Eleven minutes later Paralluelo pounced again on a poor clearance, slamming the ball into the right corner to send Spanish fans into delirium.
It appeared all over for Sweden as regulation time dwindled but Lina Hurtig headed down to an unmarked Blomqvist, who thrashed the ball in.
But Carmona broke the deadlock in a late twist, her fierce strike tipped onto the underside of the bar by keeper Zecira Musovic before bouncing down over the line, ensuring Spain create more history at their breakout World Cup.
