Rhona Martin's women curlers clinched a semi-final spot after beating Germany 9-5 in their second tie-breaker.
The British team were set to leave the Winter Olympics after losing their final group match on Monday.
They relied on Switzerland beating Germany to give them a second bite at reaching the semis.
The Swiss did just that, but Martin's team still had to negotiate two tie-breakers, first against Sweden and the second against the Germans.
They defeated the Swedes 6-4 and then booked a showdown against Canada after brushing aside Germany.