Sweden booked their place in the Women's World Cup quarter-finals after Stina Blackstenius' 55th-minute strike was enough to sink Canada at the Parc des Princes.
Peter Gerhardsson's side will face two-time winners Germany in Rennes on Saturday for a place in the semi-finals as Canada's abysmal record against European teams on foreign soil stretched to 11 straight defeats in the French capital.
Double shootout as Canada and USA see off Brazil, Netherlands
Janine Beckie missed a VAR-awarded penalty as goalkeeper Hedvig Lindahl produced a brilliant save to preserve Sweden's lead, and they were later denied a spot-kick of their own. Ashley Lawrence fouled Fridolina Rolfo inside the box, but the decision was overturned after a marginal offside call in the build-up.
During a desperately poor first half, Sofia Jakobsson had a rare sight of goal after 19 minutes when she dragged a shot from the edge of the box wide, as Canada failed to register a shot despite 61 per cent possession.
Kenneth Heiner-Moller will have been disappointed by his side's wastefulness as the ball was given away 90 times during the opening 45 minutes. But after a lot of perspiration and little inspiration, the drama spilled out in the second period.
Blackstenius kept her composure to slot past Stephanie Labbe to break the deadlock, but Canada missed the chance to restore parity with just over 20 minutes remaining as Beckie's spot-kick was kept out superbly by Lindahl.
Canada struggled to find any fluency, and they were fortunate not to concede a penalty when Lawrence's foul inside the box on Rolfo was cancelled out by a VAR offside decision.
In the ninth minute of stoppage time, Linda Sembrant blocked Lawrence's shot - and after Australian referee Kate Jacewicz checked for handball, Sweden could finally celebrate their progress to the last eight.
TALKING POINT - VAR is correctly enforced
After the farce of England's 3-0 win over Cameroon, VAR came in for quite a bit of unfair criticism when in truth, it was the match officials who lost control. Here, referee Jacewicz and Jose Maria Sanchez, the Spanish official overseeing all the VAR calls, got every decision spot on.
Sweden were correctly awarded a second-half penalty, but that was overturned by an earlier marginal offside call, while Canada were denied a late second spot-kick after the final whistle had blown as Sembrant's arm was tucked into her body when the ball struck.
Sweden: Lindahl 7, Glas 7, Fischer 7, Sembrant 7, Eriksson 7, Rubensson 7, Seger 6, Jakobsson 7, Asllani 8, Rolfo 7, Blackstenius 7. Subs - Hurtig n/a, Bjorn 6, Anvegard n/a
Canada: Labbe 6, Lawrence 6, Buchanan 7, Zadorsky 6, Chapman 7, Prince 6, Scott 6, Schmidt 7, Beckie 7, Fleming 6, Sinclair 5. Subs - Quinn n/a, Riviere n/a, Leon 6.
WOMAN OF THE MATCH - Kosovare Asllani (Sweden)
Blackstenius scored with the first shot on target of the match, but it was the brilliant vision of Kosovare Asllani that presented Sweden's top goalscorer in qualifying with the opportunity.
The 29-year-old forward scored in the opening two games against Chile and Thailand before Sweden were made to sweat over her fitness after she was withdrawn against USA.
But here, as Canada legend Christine Sinclair cut an isolated figure down the other end and VAR troubled to take centre stage, Asllani underlined her importance with a real moment of quality that reminded the 38,078 spectators inside the Parc des Princes that the world's best female footballers are still very capable of deciding matches on their own.
55 - GOOOOOOAAAAAAAAAAAAAAAL!!!!!! Sweden 1-0 Canada. The first shot on target from either side and the player that the Sweden coach Peter Gerhardsson has said is the country's most important has given Sweden the lead!!! Asllani's ball is perfect as Blackstenius peels off the back of Zadorsky and as Labbe comes out, she pokes the ball home!
66 - PENALTY? Canada won't want to go home with a whimper and they're going to give this a real go. Beckie's cross is flicked wide by Schmidt. But there was a blocked shot in the build up there. Scott's shot hits the left arm of Asllani. The referee Kate Jacewicz is coming across to review the incident...
68 - PENALTY CANADA! It could only be one outcome! Asllani is booked in the process of being deemed to have handled it!
69 - PENALTY SAVED!!! Beckie takes it, fires it to Lindahl's right, she springs across and makes a superb save!!
81 - PENALTY SWEDEN! Rolfo is taken out by Lawrence and the referee points to the spot.There was a scissor movement there, but the decision is being checked by VAR...
82 - NO PENALTY! Would you believe it! Sweden were offside in the lead-up to the penalty, and that's why the spot-kick has been ruled out. It's the right call. The right foot of Blackstenius was in an offside position.
- There will be at least five European nations in the Women's World Cup quarter-finals for the first time since 1995.
- There have been 22 penalties in 42 games so far at the 2019 Women's World Cup; as many as in the 52 games in the 2015 edition.
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