Norwegian skip Thomas Ulsrud had been in front since the first end of the tie-breaker to decide who would advance to the final four and earn a guaranteed match for a medal.
But rather than settle for a single in the final end - that would have forced an extra end in which Norway had the final stone advantage - Team GB skip Murdoch put it all on the line.
After a prolonged discussion with team-mates Greg Drummond, Scott Andrews and Michael Goodfellow and consulting with coach Soren Gran, Murdoch pulled off a sensational double take-out which secured a decisive two and a 6-5 victory.
"It will certainly go up there as one of my best shots ever," said Murdoch. "I just had to trust myself and have the courage to go for it.
"We never think about failure as a team, we only think about winning. It's a shot you don't make very often but we were confident.
"We've played these guys 100 times and the chance of stealing a point in the extra end are pretty slim. As hard as the shot was we just had to go for it.
"There was no margin for error, you couldn't be an inch wide. We just got everything right and it was a fantastic team effort.
"Our goal was to make the semi-finals and we're there and it's an amazing feeling. The standard of that game was incredible, you missed one shot and that was the game over.
Drummond was in no doubt the shot was the best call - even if the odds were heavily stacked against his skip.
"It's my first Olympics and I'm in the semi-finals. We weighed up our chances of stealing in the extra end and we decided the odds were better going for the win," he said.
"You might have a go at that shot in the middle of the game and no-one would think anything of it but to win it's different and to win to make the semi-finals of the Olympics makes it the best he's played all season."
Sweden's Niklas Edin, the in-form skip during the round-robin matches, now lies in wait but Team GB coach Gran believes the win and manner of the victory gives Murdoch's rink the all-important momentum.
"That shot meant a lot for us. We came here to reach the semi-finals and it's fantastic," he said.
"I asked the guys what they thought the best chance was to win the game and we all agreed it was it. It was a spectacular shot for everyone watching."