Although the final scoreline was tight, Muirhead and her team controlled their game against China. The Chinese started with last-stone advantage and, when Muirhead just failed to clear out the second of two opposition stones in the first end, China's skip Bingyu Wang had a hit and stay for two points.
The British team levelled with two of their own in the second and, in the third, an umpire's measure gave China one point for a 3-2 lead.
Muirhead gained an advantage in the fourth end when her last effort came tight around two guards and chipped out a Chinese stone to score two for a 4-3 lead but by the ninth end, following China's skip playing a tap-up, the score was level at 7-7.
Having last-stone advantage, however, the British knew they should keep the last end simple and they were helped when second player Vicki Adams cleared two Chinese stones out of the house. Muirhead eventually had a draw to the four-foot for the point to secure the 8-7 victory.
"I love it when my team play so great," said Muirhead. "Vicky played a fantastic double rip that really opened up that last end. It left me a draw to the four-foot which, as a skip, is a routine shot. The sweepers looked after it really well, and Anna [Sloan] called the line great - it was a real team effort."
She added: "I was really pleased with that, it was a solid performance, and we realised how important that game was. It was essential to win. Yes, we dropped our games against Sweden and Canada but they're two tough nations. We know we didn't play great, but can play a lot better if we come up against them again."
In their win over the USA, Murdoch's men netted more points without last-stone advantage - three - than they scored with last stone.
They built their lead at the start of the game, stealing a single point in the first end then a further two in the third for 3-0 after blanking the second end. By the time the game had reached the eighth end, Murdoch had a three-point lead, at 5-2.
The USA could only score a single point in the ninth end and then ran out of stones in the 10th, giving the British men their fourth win so far.
Afterwards, a delighted Murdoch said: "That was a commanding performance. I think we dominated from start to finish. We were aggressive in the first five ends and got our lead, and we were clinical after that. We had some great shot making and I thought Greg [Drummond] was on fire."
When reminded that he had more steals than 'hammers', Murdoch said: "It's not often you can say that, but it's good to see. It means we're drawing well, getting our rocks in perfect spots and causing them all sorts of trouble."
The Lockerbie-born skip, who lives in Stirling, added: "You're always trying to do better. I think we're gradually getting stronger - we'll need to be, we've got a lot of tough games to come. It's all about momentum. If we can keep going the way we are, then we're in a good place. I think we're very comfortable with the situation right now. We're up there near the top and if you'd said that at the start of the week, I'd be very happy with that. We've got a good formula going, so it's just keep doing what we're doing."
USA second Jared Zezel conceded: "Today we didn't play well enough to beat those guys, and they played great."