The GB skip had to pick her team and herself up after losing in the semi-finals to Canada on Wednesday, leaving the all-Scottish rink crestfallen and vice-skip Anna Sloan admittedly "devastated" and in tears.
After a slow start against the Swiss on Thursday, Muirhead rallied her troops to win in the last end and secure the medal that sees Great Britain at least equal their best-ever Winter Olympic medal haul from 1924 in Chamonix - four: one gold, one silver and two bronze - with the men's curling final against Canada to come on Friday.
It was also British women curlers' first Olympic medal since their coach Rhona Howie - then Rhona Martin - skipped GB to gold at Salt Lake City in 2002.
Muirhead, who skipped the British team at the Vancouver Games in 2010 as a 19-year-old, insists the bronze medal secured by her World Championship-winning rink, which also includes Vicki Adams, Claire Hamilton and alternate Lauren Gray, is only the start for them in Olympic terms.
"Ever since I was a young girl, one of my main goals was to win the World Championships," she said. "But when you do win an Olympic medal it's just as special.
"We're the youngest team here, average age of 23. We have a lot of time ahead of us.
"When we can prove we can win Olympic medals and have the maturity to do that, it shows we have a big future ahead of us.
"What a dream come true. The Olympic medal was the one medal we have been missing, and for me to win it with four of my best friends seems so special.
"But every athlete needs to learn how to lose before they can win. First, they need to learn how to get up from defeat. To lose the semi-final and know you have to come back and play for that bronze medal is extra tough, and it showed how strong we are.
"I couldn't think what it would have been like to not walk away with a medal around our necks.
"We regrouped and came out fighting, and I knew we still had a chance to get a medal. I'm delighted."
Muirhead was coolness personified as she delivered her last stone, but she was glad not to be aware of the significance of the medal win in the context of Great Britain's Winter Olympic history.
"I didn't realise that," she said, smiling as she added: "I'm glad no one told me that before I played it.
"What a fantastic Olympics for Great Britain.
"To hear that stone made it one of the most successful for Team GB will make that stone stay with me for a lot longer."
Sloan reiterated the sense of togetherness within Muirhead's group which ensured they would not return from Russia empty-handed.
"I think it shows the team spirit and the support we have for each other to come back from that loss, pick ourselves up and get ready for today's game, because there was no way we were going to leave without a medal," she said.
"We all wanted it so bad. We wanted the gold, there is no doubt about that, but it shows the spirit to make sure we go home with a medal and a bronze medal feels amazing right now.
"It was hard to pick ourselves up but that's curling, things happen like that.
"But we knew if we put in a performance like yesterday and more, then we would get a win.
"We've worked so hard over the three years and I truly think we've deserved that medal."
Vicki Adams was "still in shock" minutes after the final end, but was clear as to how well GB had worked to set up the dramatic finish which allowed Muirhead to slide in a final shot to take the medal.
"I feel absolutely amazing," said Adams. "I knew if we went into the last end with the hammer we could pull it out.
"We played the end the best we could.
"Eve played a fantastic shot at the end, after Claire played two fantastic shots.
"We couldn't have set it up any better and for Eve to have a four-foot draw at the end was great."