A win over the Czech Republic and defeat to Canada leaves Scotland fifth in the standings and on track for Olympic qualification.
A hard-earned 6-5 win over the Czech Republic in the competition's 14th session had kept them firmly on track for a top-six spot, which would seal Olympic qualification for next year's Games in Beijing.
Having burst into a 4-1 lead Scotland were pegged back to 5-5, but with last stone advantage Muirhead earned the vital point that secured their fifth victory of the Championship.
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But a similarly close encounter with hosts Canada went the other way, with Muirhead and teammates Vicky Wright, Jen Dodds and Lauren Gray recovering from a 5-3 deficit to force extra time but ultimately falling 6-5 at the death.
Muirhead - who scooped bronze for Team GB at the 2014 Winter Olympic Games - said: "We're obviously gutted with the end result there. We played such a fantastic game, but had one bad end at the eighth and gave up a big steal, which cost us unfortunately.
"We played the best game we have all week against Canada and put them under a lot of pressure, but just didn't manage to hold it out to the end and convert it."
With five wins and three defeats to their name so far Scotland face Switzerland in their next bout of round-robin action, who sit second in the standings having lost just one match.
And with a clash against Estonia - who have won just once so far in the competition - to come on Wednesday too, 2013 World Championship gold medallist Muirhead is confident of success on day six in Calgary.
She added: "The good thing is that it shows we can play very, very well, so we just need to take that into tomorrow, try to concentrate on how we really did play and move on."
Team Muirhead will take confidence from the fact that defending champions Switzerland suffered their first loss of the Championship in Tuesday's opening session, 8-3 to Sweden in a repeat of the 2019 final.
Elsewhere in session 13 there were also wins for Korea, Canada and table-toppers Russia, while the latter joined Scotland, Denmark and the United States in triumphing in the day's second round of matches.
Alongside Canada, the United States and Italy rounded the day off with wins in session 15, while Switzerland bounced back from their earlier defeat by seeing off the Czech Republic 9-1.
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