With three tricky games to come in the round-robin stage, Mouat’s rink have five of the six wins they need to guarantee a shot at a medal on their Games debut.
The fifth victory was the toughest yet and relied on the skip delivering a clutch last stone, chipping out a red Swiss stone.
“We needed to come out and win that one to keep our hopes for the play-offs alive, so it was a big game,” said Mouat, 27.
“They had their backs against the wall and were going to give us a good fight regardless of what was happening elsewhere.
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“I'm very happy to get over the line with that one and to play well too.”
On the last stone, Mouat added: “Obviously I had a bit of nerves. It was basically just trying to throw it as hard as I could and give it to the sweepers!
“I tried to throw it half-stone and let Bobby (Lammie) take it back a wee bit and that's exactly what he did. I always feel confident when Hammy (McMillan) and Bobby are standing by.”
It was a very cagey start with the first end blanked and both teams taking just one with the hammer in the second and third.
A superb draw into the button saw Mouat take the first two of the match and go 3-1 up.
There was a rare mistake from the skip in the sixth end as a miss allowed the Swiss to steal one and find a foothold once again.
Britain also passed up the chance to blank the seventh end when Mouat was narrowly unable to take out a third red with his penultimate stone.
But he hit back in the eighth, using his own stone to chip out the Swiss and Benoit Schwartz’s runback takeout failed to come off, allowing Britain to steal one back.
The game swung back the other way when Mouat clean missed a takeout with his last stone of the penultimate end and allowed Peter de Cruz to lie two.
Vice-skip Grant Hardie said: “We started off and the game-plan was excellent. We got the hammer and the jump into a 2-0 lead and really controlled the scoreboard.
“The plan was to continue that in the sixth and we unfortunately gave up a steal and had to regroup and start again. We had to play some really good ends to close it out.
“The aim is always to have hammer coming down the last end, which we were able to do and Bruce made that great shot for the win.”
Now Mouat’s rink face their toughest round-robin tests, in the shape of the other three teams who have set up shop in the top four and are on course for the semi-finals.
Hardie said: “We knew the importance of that game coming in knowing we have three very tough games to come.
“Hopefully we can kick on now and secure our spot in the play-offs tomorrow.”
A titanic tussle with Niklas Edin’s world champion Swedish rink is followed by the Russian Olympic Committee, who have come closer than anyone to beating the Swedes, and Canada.
Edin made it six wins from six with a 7-5 triumph over the Russian Olympic Committee, but Mouat has the Swede in his sights having won the final of November’s European Championships
“I think we've got a really good track record against them this season,” said Mouat.
“We've played them quite a few times this season, so we just need to come out and play well, which I feel like we're doing.
“They're doing the same because they're undefeated so far. We're going to try to do what we do best, which is playing very technical tap shots, so we'll see what we get tomorrow.”
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