Eve Muirhead's team took some time to get into their stride at the Ice Cube Curling Center.
After a blanked first end, Mirjam Ott's team took a two in the second to put GB on the back foot.
A double take-out in the third end by Switzerland ultimately led to Muirhead having to take just one point before passing the hammer - the last shot of each end which is normally decisive - over to Ott.
Another great double take-out, this time from Muirhead with her first shot in the fifth end, allowed GB to go into the interval level at 3-3.
Switzerland edged ahead again 4-3 and Muirhead blanked the seventh to get another chance with hammer to go for two points to get in front for the first time in the game which they did, but only after a measurement was used to confirm one of the British stones was indeed closer to the centre than the nearest one from Switzerland
GB went into the 10th end level but importantly with hammer which, in the end, provided Muirhead the opportunity to roll up the final stone with some ease to claim the historic victory.