The Scots had control from the start of the game, scoring two in the opening end, but they could not shake off the Canadians who were able to score a two of their own in the second end when Muirhad's take-out of a Canadian stone jammed.
In the third end, Muirhead played a nose-hit to score two points for a 4-2 lead but in the next end, Canada got two points back when their skip Rachel Homan also played a precision hit.
Muirhead could only take one point from the fifth end, with a hit and stay, and then Canada's Homan scored one point with a pressure draw against three Scottish counters in the sixth end to tie the score at 5-5. Scotland then moved ahead again, to 6-5, when Muirhead played a nice draw in the seventh end.
The Scots had two slack shots in the eighth from second player Adams and third Sloan and this put them into trouble. Canada were eventually able to draw for two and take the lead for the first time in the game, at 7-6.
In the ninth end, Homan played an important double take-out with her last stone, forcing Muirhead to score just one point with a nose-hit to level the game at 7-7.
In the 10th, Muirhead promoted one of her own stones to tap out a Canadian counter and this left her lying two shots as Canada's Homan came to play her last shot.
However, what looked like a fairly easy double take-out attempt to score just the one point needed for their win ended up too straight and jammed one of the Scottish stones. This gave Scotland the first steal of the game and scored the one point needed for the win that put them into the final. The Scots also beat Canada in the round-robin last weekend in their first game of the whole championship and have now only been beaten by one team in the whole week – today's opponents Sweden.
Afterwards, a smiling Muirhead said: "I'm delighted with that. I think it was a real high quality game, but when it comes down to last stone like that, I tell you what – I'd rather be playing than watching because I'm not the best watcher. We always have good battles, Rachel and I, and it just shows you that was a good battle.
"I don't think I could have made my last stone any better. The girls set up the end well. Leaving her a big double hit is probably not ideal because she loves that shot, but when the pressure's on, it make it tougher for anyone."
Looking forward to the final, and mindful that she was beaten by Germany in the only previous world final she has played, in 2010, she added: "I don't want to come away with a silver. Making the final's great but when you've already got one silver medal from a final, you don't want another one, so we'll be definitely pushing hard for the gold."
Canada now go on to face USA this morning for bronze medals. Canadian third player Emma Miskew said: "I think we played really well and we deserved it but it sucks it came down to that – but what are you going to do? They made a nice shot and it was a tough one."