In sweltering conditions at the Parc des Princes, the two teams struggled to register any shots on target in a first half despite Canada dominating possession.
That all changed after the break when the Swedes stepped up a level and they were finally rewarded in the 55th minute when the Canadians lost possession of the ball in midfield.
Kosovare Asllani played an inch perfect diagonal ball to striker Blackstenius, who prodded the ball past onrushing keeper Stephanie Labbe.
It was her first goal of the tournament and it freed the Swedish team, which almost added a second with a thunderous drive from Fridolina Rolfo in the 61st minute.
Canada had a chance to get back into the game after 68 minutes when they were awarded a penalty after a lengthy VAR review ruled that Asllani had handled the ball.
However, veteran Sweden keeper Hedvig Lindahl dived to her right to tip Janine Beckie's spot kick away.
"If they doubted I could make any penalty saves, that proved them wrong," Lindahl told reporters. "I had to stretch fully and it worked. It was pure joy. We got a lot more energy because of that."
The save appeared to suck the spirit out of the Canadians who struggled to create much beyond a few half chances and Asllani almost scored for Sweden five minutes from time as she volleyed in from a corner, but her shot was cleared off the line.
It was the first time Canada had failed to score in a World Cup knockout match and coach Kenneth Heiner-Moller said his young squad would learn from the experience.
"We have a lot of players with a bright future. They didn't get their chance, but it's given them a thicker skin. The way we develop players is important. We have the third youngest squad so it's looking bright," said.
Sweden will now face two-time champions Germany on Saturday in Rennes in a repeat of the 2003 final. The Swedes have not beaten the Germans since 1995.
"What's happened years ago isn't interesting. We have to look at how Germany played the last three matches," Swedish coach Peter Gerhardsson told a news conference.
"I don't think it's relevant to the players, but it will be nice to break that trend."
(Reporting by John Irish; Editing by Ken Ferris and Pritha Sarkar)
