Germany opened the scoring in the 16th minute when Magull flicked an incisive Sara Dabritz pass up to waist height before swiveling on her left foot and firing home with the right to beat a helpless Hedvig Lindahl.
Schult did well to turn away a powerful header by Fridolina Rolfo but the rebound fell kindly to striker Blackstenius, who fired home from point blank range for her second goal in as many matches.
Marozsan later missed a flawless chance to force an extra time after heading wide in the 80th minute and the Swedes held their nerve to reach their fourth World Cup semifinals. The United States plays England in the other semifinal Tuesday.
Sweden's players celebrate at the end of the France 2019 Women's World Cup quarter-final football match between Germany and Sweden, on June 29, 2019, at the Roazhon park stadium in Rennes, north western France.
Germany had beaten the Swedes in the 2003 Women's World Cup final and more recently in the 2016 Olympic gold-medal game in Rio de Janeiro. I felt it, but still, we won.
"There's not a single mitochondria in us that's content. 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.
"We have talked about the possibilities here for us to go far and win every game", said a bullish Sweden coach Peter Gerhardsson.
"I think we have very good players but things have changed so much since the European Championships".
There were tears on the faces of numerous Germany squad as the reality of their exit - and Olympic absence - hit home hard. "This should not happen like it did", said Magull. However it was the Dutch who responded best to the on-pitch humidity, with temperatures creeping over 30 degrees Celsius, completely dominating the second half in an impressive display that will give whoever wins later on Saturday pause for thought. That's a real shame.
"We knew we had to threaten them behind their back line".
"That brings the danger of conceding on the counter, which had happened before the break". Earlier, the Netherlands reached the semi-finals for the first time in their history after Vivianne Miedema and Stefanie van der Gragt scored in a 2-0 win over Italy in Valenciennes.
The Swedes had last claimed a tournament win over Germany at the 1995 World Cup but here they came from behind to triumph in an enthralling game played in ferocious heat. Sweden will join the Netherlands and Great Britain - who have qualified thanks to England's World Cup run - at the Games instead.