Linda Sembrant's stoppage time winner broke Belgian hearts as Sweden won 1-0 in Leigh on Friday to set up a Euro 2022 semifinal with hosts England.
The Olympic silver medallists were strong favourites to progress against a Belgian side playing in their first ever knockout game at a major women's tournament.
However, the No 2 ranked side in the world were frustrated by Belgium goalkeeper Nicky Evrard, poor finishing and a controversial VAR review for 92 minutes until Sembrant made the breakthrough.
"I think it's a game where we were in control," said Sembrant.
"They made it really hard because they made it very tight in front of the goal, but in the end we got that goal that we needed."
Sweden's preparations had been hit by a trio of positive coronavirus cases for Jonna Andersson, Hanna Glas and Emma Kullberg.
But they still dominated from start to finish with 34 attempts to Belgium's three.
The Belgians had surpassed expectations just by making it through the group stages for the first time in only their second major tournament in the women's game.
"We were the underdogs from the beginning but we did really well as a team," said the Red Flames' captain Tessa Wullaert.
"That's what I want to remember from this tournament."
Filippa Angeldal forced Evrard into the first of a series of saves inside the first 10 minutes.
The Manchester City midfielder, who scored twice in Sweden's 5-0 win over Portugal in their final group game, then fired over with a clearer opening from the edge of the box.
Sweden thought they had made the breakthrough on 26 minutes when Stina Blackstenius coolly slotted past Evrard from Kosovare Asllani's through ball.
However, for the third time in the tournament, the Arsenal striker was denied by a VAR review for offside which harshly ruled the goal out.
The fluency of Sweden's attack disappeared after the break as they struggled to break through the mass ranks of Belgian defence.
Set-pieces then became the biggest threat from Peter Gerhardsson's side.
Blackstenius should have scored when she headed too close to the excellent Evrard.
The Gent goalkeeper was even equal to Nathalie Bjorn's effort in the final minute of stoppage time, but the rebound fell kindly for Sembrant to smash the rebound home and spark wild scenes of celebration among the Swedish squad.
"I felt the tears coming because I was so happy," said Sweden defender Magdalena Eriksson.
"It was a frustrating evening. To finally get that relief, oh my God. I'm so proud of all the girls for how hard we fought."
Sweden have not lost in open play since March 2020.
But they face a huge step up in quality against England in front of a 30 000 capacity crowd in Sheffield on Tuesday.
"I know all the players, extremely talented players," added Chelsea defender Eriksson.
"England have been amazing in the tournament so far. We have to be really on it. It's about recovering and getting fresh again."