Muirhead, alongside Anna Sloan, Vicki Adams and Claire Hamilton, was devastated after a semi-final defeat to Canada meant there would be no Olympic gold to add to their world title.
But less than 24 hours later, they responded with a tactically brilliant 6-5 win over Switzerland's Mirjam Ott, Muirhead delivering a textbook final stone - under the most extreme pressure - to secure the victory.
"It's a dream come true, this is the medal we've been missing and to win it with four of my best friends feels so special," she said.
"That shows what great athletes we are, you have to learn to lose before you can win and get back up from a defeat. To lose a semi-final at the Olympics and then come back and play for bronze is extra tough. We regrouped and came out fighting.
"I'm mentally buzzing, it's been a constant rollercoaster, we've had some tough losses and great wins and many of the games have come down to last end, last stone. To end on a high makes it even better. I couldn't think of what it would have been like to walk away without a medal around my neck."
Sloan insisted she was always sure that Muirhead would deliver her final stone to perfection, despite the jangling nerves of those present.
All four members of the rink had played a perfect final end to outsmart the canny Ott, a two-time Olympic silver medallist, and her team.
"I never had any doubt when Eve was over that last stone. We played a great last end and it was such good team effort," she said.
"Eve always says give me a draw and I'll make it and it was such great team effort.
"We were devastated yesterday and it shows our team spirit that we could rebound from that loss. There was no way we were leaving here without a medal. We wanted the gold but it shows the spirit of our team to pick ourselves up and a bronze medal feels amazing right now."
Muirhead and team-mates won't defend their world title in Beijing next month but she is predicting a bright future, with veteran Ott insisting it's only a matter of time before they upgrade their bronze at future Games.
"We're a young team with a lot of time ahead of us," said Muirhead.
"We're the youngest team here, our average age is 23 and we've got a big future ahead of us. Curling gets a lot of attention every four years and for us to increase that, we've got to win medals."
The bronze medal means Team GB have now equalled their best ever performance at the Winter Olympics, a record dating back to the 1924 Games in Chamonix. And if David Murdoch can win curling gold in Friday's final it will officially be the best ever.