Eve Muirhead (pictured) of Scotland and Norway's Thomas Ulsrud both won their Page 1-2 play-off games.
The Scottish women were up against Russia's Liudmila Privivkova and finished the game in spectacular style in the ninth end.
Muirhead was looking like she would give up a second successive steal, with three Russian counters in the house as she faced her last shot.
Not only did she remove all three, she took out another Russian stone for good measure as her own shooter stayed around to count four to Scotland.
The stunned Russians then conceded the game at 9-4 to Scotland.
The Scots now move on to the final, while Russia face Sweden's Stina Viktorsson - who beat Switzerland's Mirjam Ott by 5-3 in the Page 3-4 game - in today's semi-final.
The Swiss will next appear in tomorrow morning's bronze medal game.
After her terrific winning shot, an elated Muirhead said: "We deserved to win that game.
"We were up most of the way and got our twos and forced ones and they came back strong in ends eight and nine, and to finish as we did I'm really delighted."
Speaking about the pressure Russia applied in the second half, she added: "I'm not going to lie - they really stepped up and we had a few slack shots, but when it came to that shot in the ninth, it was do or die.
"The triple was set up, but I didn't see the quadruple coming.
"To finish with a four and kill the game, that's good."
Ulsrud's victory for Norway over Christof Schwaller of Switzerland was less spectacular.
He came from 1-2 down at halfway to score in three successive ends and move into the lead, eventually sealing his 5-4 win with a single score in the tenth to make it to the final.
"It feels really good to be in the final," said Ulsrud.
"I think all our guys have a real goal.
"We've never won anything – we've got a lot of medals, silver or bronze, but we've never won gold, so we have a chance on Saturday."
The Swiss will now face Denmark's Rasmus Stjerne in the semi-final today, after Denmark beat Germany's Andi Kapp by 10-5 in the page 3-4 play-off.
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