Norway led by one and were lying shot but Murdoch, after taking a time out to work out every angle and consider whether to risk going for the win or playing safe to take the match into sudden-death, sent down a perfectly calculated final stone that sent another British stone ricocheting into the Norwegian counter, giving Britain two, and the match.
Britain will now play Sweden in the last four on Wednesday, with Canada taking on China in the other semi.
Earlier in the competition Britain had looked safely on course for the semis but lost their last three group games, including one to 2010 silver medallists Norway, forcing them into the playoff.
"The standard of that game was incredible," said Murdoch.
"But we are not scared of going for the big shots."
Britain's women are also through to the semi-finals, also on Wednesday, but face a tough task against a Canadian team who won all nine group games. Sweden and Switzerland meet in the other women's semi.
(Editing by:)
