Skip Eve Muirhead led GB's fightback, from a terrible start to the match, to book her place in her first Olympic final at the fourth time of asking, along with team-mates Vicky Wright, Jennifer Dodds and Hailey Duff.
They join Bruce Mouat and the men's team in guaranteeing a medal in the finals at the National Aquatic Centre over the weekend.
Japan await in the women's gold medal match after beating Switzerland 8-6.
Muirhead's attempted draw with her last stone of the first end finished almost two metres short and gave Swedish skip Anna Hasselborg the simplest chance to roll in for a four.
Immediately it looked like the Britons might be facing a repeat of their heavy semi-final defeat to the same team in Pyeongchang four years ago, when they failed to recover from a poor start and lost 10-5.
But Muirhead hit back strongly by taking three points in the next to give her team hope, and two single ends in succession hauled her back level at the halfway stage, albeit with Sweden retaining the 'hammer' advantage.
Hasselborg pressed back in front with a two-point end in the sixth, but errors were becoming more prevalent in the Swedes' play and a missed double take-out attempt in the next gave Muirhead the chance to roll in for two to level at 7-7.
A packed eighth end resulted in Hasselborg having to settle for taking a one, before Muirhead produced a magical shot to take four in the ninth.
Hasselborg responded in kind to brilliantly take three and force an extra end. Britain held the 'hammer', or final stone, but Muirhead did not need it as Hasselborg's attempt with her final stone drifted wide and gifted the Britons the point they needed to seal a stunning win.
Muirhead admitted she was desperate to avoid another semi-final disappointment.
"It's third time lucky for me," she told the BBC. "I've lost two semi-finals before and I was desperate for it because these opportunities and these moments don't come around very often.
"I'm so, so proud of these guys. It's such a team game out there. I'm pretty speechless right now but it sounds amazing to say 'we're in the Olympic final'.
"We've got tomorrow off so we'll take tonight to celebrate among ourselves.
"We'll be here supporting the men tomorrow and then we need to knuckle down. We've still got one game to go and, when you get to that final, no one wants to come away with a silver medal."
Team-mate Dodds spoke of the spirit among the team to come back from the shock of going 4-0 down after the first end.
"We knew it was going to be tough," she said. "I think I did say, if we were going to lose a four, to lose it in the first end and we did.
"None of us put our heads down, we all rallied around each other and that's such an important part of curling."