By Agence France-Presse
Sweden had not beaten Germany at a major women's tournament since the 1995 World Cup, failing to win any of their subsequent meetings at World Cups, European Championships and Olympics in almost quarter of a century.
That run included defeats in the 2003 World Cup final and the gold medal match at the 2016 Rio Olympics, but they gained revenge in Rennes, coming from behind to win their quarter-final 2-1.
Lina Magull had given Germany a 16th-minute lead with a fine finish from a Sara Daebritz assist, but the excellent Sofia Jakobsson equalised soon after on a hot evening in Brittany.
The winner arrived three minutes after half-time, with Blackstenius prodding home the rebound after Almuth Schult had saved a Fridolina Rolfo header.
Despite bringing on star player Dszenifer Marozsan, who had missed the previous three games with a broken toe, Germany remained blunt as the clock ticked down.
Blackstenius had scored Sweden's winner against Canada in the last round and also netted against the Germans in that Olympic final defeat in 2016.
"We have talked about the possibilities here for us to go far and win every game," said a bullish Sweden coach Peter Gerhardsson.
"There's not a single mitochondria in us that's content. We're going to go for it."
The Germans will now be deprived of the chance to defend their Olympic title, with defeat here meaning they fail to qualify for the 2020 Tokyo Games. Sweden will join the Netherlands and Great Britain -- who have qualified thanks to England's World Cup run -- at the Games instead.
"We are now qualified for the Olympics. That is one thing that has been hanging over our heads for a while," said Gerhardsson.
Germany coach Martina Voss-Tecklenburg told ARD: "The defeat hurts, but we are in a process. We will grow from this experience."
Sweden go on to a semi-final encounter with the Dutch in Lyon on Wednesday, and they will have a score to settle there too, having lost to the Netherlands at Euro 2017.
The 'Oranje' went on to win that tournament and have coped well in France with their status as reigning European champions.
- 'Dream come true' -
On Saturday they sank Italy 2-0 in Valenciennes as headed goals from Vivianne Miedema and Stefanie van der Gragt in the second half taking them through to their first ever World Cup semi-final in just their second appearance at the tournament.
"I am very proud of the team. We have very good players. Since our victory at Euro 2017 we have gained a lot of confidence and we have improved enough to do well at this World Cup," said Dutch coach Sarina Wiegman. She said qualifying for the Olympics was "a dream come true".
Miedema's goal means the Arsenal striker -- her country's record goal-scorer -- now has 61 in 80 international matches.
Surprise quarter-finalists Italy wilted towards the finish on a hot day and their players were in tears at the end.
"We are really upset because we got this far and had the chance to qualify for the Olympics. That's what we dreamed of," said Barbara Bonansea.
"No-one expected all this from us so we can't be anything but happy."
The tournament now switches for the closing stages to Lyon -- home to Europe's top women's club side -- with holders the United States and England facing off in the first semi-final on Tuesday.
Megan Rapinoe's double strike gave the USA a 2-1 win over France on Friday, ending the hosts' dream of winning the trophy on home soil.
England reached their second successive World Cup semi-final with a straightforward 3-0 win over Norway on Thursday.