Having beaten Germany 7-2 in the morning session on day six in Beijing, China, Scotland took to the ice again later that evening, knowing that a victory would see them advance to the play-offs.
However, the Czechs were also eyeing up a spot in the play-offs and were refusing to give in, coming back from 3-1 down after the fourth end to level the scores at 3-3 after the fifth.
Both teams then got their noses in front, with Muirhead putting Scotland 4-3 to the good before Czech skip Anna Kubeskova scored two points in the seventh end to turn the tables.
But in the with her final effort in the tenth end Muirhead took out a Czech stone at the back of the house to score two points, and with it secure a 7-6 victory and the fourth play-off spot.
Scotland will now face Sweden in the Page 3-4 play-off game on Saturday, and Muirhead is champing at the bit to get going.
"We've ticked that box after this vital win," Muirhead said. "That was a good game, she played some cracking draws to keep them in the game.
"We were patient, which was key out there. The ice was tricky, the trickiest it’s been, but we adapted to it pretty quickly.
"We were at the stage that win, win, win was what we had to do. Our first goal was to make the play-offs and we’ve ticked that box.
"Our next goal is to make the semi-final and onwards from there."
Elsewhere in the session, Russia beat China 6-4, putting them in the Page 1-2 game for the first time, where they will take on unbeaten Canada, who have won all 11 of their games.
Denmark managed to pick up a victory in their final effort as after ten losses they beat Italy 8-7, while South Korea squeezed past Switzerland 9-8.
Read the original article on Eurosport: Scotland reach World Women's Curling Championships play-offs