Jackie Groenen struck the victor in the 99th minute of play at Stade de Lyon.
The Americans were indebted to goalkeeper Alyssa Naeher for saving a late penalty in their 2-1 semi-final win over England on Tuesday.
Peter Gerhardsson's ladies had momentum after the half-hour mark and they almost broke the deadlock eight minutes before the break as Hurtig latched onto a close range chance in a goal-mouth scramble but van Veenendal was able to keep the Oranje in the game with a crucial save.
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It was a simmering second half right from the onset as both teams realised that a solitary goal could very well be the difference.
In the second, Nilla Fischer came close to giving Sweden the lead in the 55th minute, getting the ball off a scramble following a corner kick and firing a low shot that hit the goal post.
But both goalkeepers, and the woodwork, played a part in a goalless 90 minutes as they held firm under aerial bombardment from the flanks and set-pieces. Miedema's 61 goals in 80 worldwide matches are the most in Dutch history, male or female.
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He spent the second half of the 2017/18 season on loan at Fulham , and was part of the side that beat Villa in the Sky Bet Championship play-off final.
Then again, that was not the best save in the second half, with Sweden's Lindahl displaying stunning athleticism to tip a Vivianne Miedema header onto the bar soon after. She finished precisely from 20 yards.
The Netherlands had to replace Lieke Martens, still suffering with a toe injury, with Jill Roord at the break but then the match began to open up.
Saturday's 2-0 victory over Italy in the quarter-finals has totally changed the mood with the result also securing the Dutch their first Olympic qualification. We had more control and they had some chances, but we have a good goalkeeper in Sari and she made some really nice saves.
There was no immediate update on her condition.
Holland's Jackie Groenen believes the United States can be beaten after firing her country into the World Cup final.
Sweden coach Peter Gerhardsson understood.
Extra time approached, although substitute Shanice van de Sanden might have won it in stoppage time had her powerful strike not been tipped over by Lindahl.
"I feel empty right now, whether that has to do with the match or Kosovare, I am not sure, but that is how I feel".