Sweden's players celebrate at the end of the France 2019 Women's World Cup quarterfinal match against Germany
After enjoying an early spell of possession, midfielder Lina Magull put the Germans in front in the 16th minute with an acrobatic volley through the legs of Swedish goalkeeper Hedvig Lindahl.
Germany had not conceded a single goal in this tournament but that changed when winger Jakobsson latched onto a long ball straight down the middle from Linda Sembrant, and slotted home past goalkeeper Almuth Schult.
German coach Martina Voss-Tecklenburg threw on midfielder Dzsenifer Marozsan, who had not played since breaking a toe in their tournament opener against China, at the start of the second half but it was Sweden who took a shock lead.
Schult did well to turn away a powerful header by Fridolina Rolfo but the rebound fell kindly for striker Blackstenius, who fired home from point blank range to get her second goal in as many matches.
Marozsan missed a glorious chance to force the game into extra time when she headed wide with the goal gaping in the 80th minute but Sweden held their nerve to reach their fourth World Cup semifinals.
The win was Sweden's first over Germany at a major tournament since 1995, having previously come close in the finals of 2003 World Cup and 2016 Rio Olympics.
Sweden's semifinal opponents were confirmed earlier in the day when Netherlands defeated Italy 2-0 in Valenciennes, courtesy second-half headers from Vivianne Miedema and Stefanie van der Gragt.
Netherlands, Sweden, along with Great Britain - after England reached the last four on Thursday - have qualified for the 2020 Olympic Games in Tokyo as the top three European teams at the World Cup.