Japan's win guarantees Asia will have two teams on the medal podium with South Korea taking on Sweden in the gold-medal final on Sunday.
"It's the first medal for Japan so it's history," smiled Japan's Canadian coach J.D. Lind. "That is something this country has been trying to do since the Nagano Olympics so to finally get to do that, it's a huge day for sure.
"It's been stressful, I definitely feel for Eve Muirhead's team. They had a shot to win. I feel for her having to miss but that's curling and we'll take it."
The match was a tight, defensive, tactical affair from start to finish with neither rink putting up more than one point in an end.
The first mistake came in the ninth and fell to British skip Muirhead who missed on a takeout on her final rock, allowing Japan to steal a point and nose in front 4-3.
Britain needed a point to force extra ends but Japan stole another one when Muirhead misfired on her final stone trying to double the two Japan rocks out and keep hers in.
"Of course I am absolutely gutted. As a team we gave it everything, we didn't leave anything out there," said Muirhead, winner of a bronze at the 2014 Sochi Olympics. "As a skip it is hard to take when you have a shot to win.
"The shot was there, that's why I went for it. Curling comes down to inches and if that had curled another centimetre we would have had the bronze medal around our necks.
"It's going to be hard to take, I'm devastated.
"Having a bronze medal before and coming away with nothing is hard. This is going to take a bit of time."
(Editing by Clare Fallon)
