The Scottish quartet were in command throughout against the Germans, leading 5-2 at the break before accelerating clear, but the hitherto unbeaten Swiss proved more obdurate opposition.
Mouat’s men led 3-2 at the break – a steal in the third proved the difference – and it took until the seventh end for either side to register a score greater than one.
It was the Swiss who did it, to lead 4-3, but it all came down to the last end.
Britain needed one to tie, two to win. They had to settle for the former, meaning an extra end. But Switzerland had the hammer and they held their nerve to close out a statement victory.
“On another day we come away with the win,” Mouat told BBC Sport.
“It’s going to be tough to beat them but we know we are playing pretty well and it would be exciting to play them again.”
Earlier in the day, Britain’s women were unable to repeat their statement win over Canada against the Swedish rink who denied them European gold in November.
The unbeaten Swedes raced out to a 7-3 lead at the break – after twice scoring three with the hammer – and stole one in the sixth to take a stranglehold on the game.
Rebecca Morrison’s rink kept fighting but ultimately fell to a 10-7 defeat to leave their semi-final hopes in the balance.
At least four wins will be required from their final five round-robin matches to have any hope of reaching the knockouts.
“It’s really hard at this level – it’s near-misses and we’re a couple of centimetres away from making great shots,” Morrison told BBC Sport.
“It’s frustrating but that’s what happens at the Olympics. You need to be at your best and we just weren’t quite there.”
The women are back on the ice against Denmark (08:05 GMT) and Switzerland (18:05) on Monday, while the men face Norway (13:05).
Anastasia Vaipan-Law and Luke Digby safely progressed to the final round of the pairs figure skating after recording a season-best score.
The duo, who are the first British representatives in this Olympic event since 2014, endured a troubled build-up to the Games after Digby suffered a wrist injury which limited their ability to practice lifts.
And in the team event at the start of the Games, Vaipan-Law suffered a fall during their throw triple Salchow, meaning there were worries about whether they would finish in the top 16 of the short program – needed to qualify for the free skate.
But they assuaged those doubts with a slick routine as Vaipan-Law landed the throw well before their final spin was synchronised perfectly.
Digby was grinning even before their routine concluded, and was proven right as they scored 66.07, their highest score of the 2025-26 season.
“That little celebration at the end was me releasing all the emotion of it going exactly as I wanted it to,” Vaipan-Law told the BBC.
They qualify in 13th place, meaning they will perform fourth in the free skate tomorrow – and will aim to better their best World Championship finish of 12th.
“Seeing so many British flags, that energy gave us a little extra,” said Digby. “We kept our heads and we were nice and calm. A clean skate, we couldn’t ask for any more at the Olympics.”
Germany’s Minerva Fabienne Hase and Nikita Volodin, who last year won world silver, lead at the half-way point with a score of 80.01.
European champions Anastasia Metelkina and Luka Berulava are second as they aim to win a first-ever Winter Olympic medal for Georgia, while Canada’s Lia Pereira and Trennt Michaud are currently in bronze position.
