Muirhead was pushed all the way by Danish skip Lene Nielsen eventually running out victorious 8-6 to remain top of the standings along with Sweden who also won, defeating Japan 9-4.
Denmark took a 2-0 lead in the second end, however Muirhead drew into a busy house in the third for three points then scored the same amount with a delicate tap out in the seventh.
Nielsen responded with a hit for one point in the eighth and attempted a split with her last stone although it was unsuccessful as Scotland secured their seventh straight win.
Muirhead moved one step closer to securing a place in the latter stages with the victory but acknowledged that her Scottish rink were not at their best against Denmark.
"We knew we were going to have to come out with our A game but we were a wee bit slacker early on and it cost us a few here and there," said Muirhead.
"The good thing from that game is that we all stick together, we all make the key shots when we have to. We just weren't as sharp as we had been the day before.
"In any major championships you can't have slack games. We just weren't quite as sharp, it wasn't bad, we knew it was always going to be tough against Denmark but overall we're still happy."
Nielsen bounced back from the loss to Muirhead by beating Italy 9-7 while Germany were on the receiving end of two defeats, the first 8-5 to Canada and the second 7-3 to Switzerland.
Japan went from their defeat to Sweden to a 10-3 loss to Russian skip and European champion Anna Sidorova, who kept the pressure on the top two with her record now six wins and two losses.
And USA skip Erika Brown went from a 9-2 victory over winless hosts Latvia after six ends in the morning session to a 9-5 loss to Wang Bingyu's China who scored five points in the final end.