Eve Muirhead's team entered the final end all square at 5-5 but with the benefit of holding the hammer after conceding one shot in the ninth end, and successfully picked up a shot in the final end to claim bronze for Muirhead, Anna Sloan, Vicki Adams and Claire Hamilton.
Swiss skip Mirjam Ott left Muirhead a straightforward draw to the centre with the final stone, and the 23-year-old came through with flying colours to add Olympic bronze to her world championship title.
"It was a great game, it could have gone either way," said Muirhead.
"We felt like we were chasing it a bit in the first half, then we stepped it up - and we had to.
"This means so much. After the disappointment of the semi-final we immediately said we can't feel like that again, we wanted this medal so badly.
"When you look at our success over the last couple of years, the one medal we were missing was the Olympic medal and we have got that now.
"I am so happy, we are all pushing each other and it makes it more fun to win something," she added.
It secures a fourth medal for the British team in Sochi, making these the most successful Winter Games since 1924.
And if David Murdoch and his men's curling rink upgrade guaranteed silver to gold tomorrow, it will be the best ever and there are still more chances to come.
Great Britain's four-man bobsleigh team were quickest in training on Thursday morning, and Elise Christie is a serious medal contender in Friday's 1000m short track speed skating.
Muirhead admitted there were some tough words exchanged after a semi-final defeat to Canada had cost the world champions the chance to add the Olympic title to their resume.
But alongside fellow Scots Sloan, Adams and Hamilton, she got her tactics spot-on to defeat Switzerland's Ott, a two-time silver medallist.
Muirhead admitted the feeling was relief after finally winning the only medal missing from her collection, though her youthful rink will surely be back and looking for another upgrade in four years' time.
Ott beat the British skip in the round robin stages and took an early lead in the bronze medal match, which was a cagey, tactical, low scoring and utterly absorbing affair.
Muirhead's rink all recorded high percentages and went into the final and decisive end tied at 5-5, but with the critical advantage of the final stone.
Ott is a canny operator but Muirhead is just as smart and her team are well drilled to listen and deliver on her instructions.
Muirhead will have played the regulation shot she had to win the bronze time and time again in practice, without a problem.
Ott's yellow stone was holding advantage but Muirhead got her final delivery inch perfect and once again the tears flowed just as they had after the match against Canada - though this time it was relief rather than frustration.