Muirhead and her colleagues Hailey Duff, Jennifer Dodds and Vicky Wright beat Anna Hasselborg's Olympic gold medal-winning quartet 7-4 in the women's final as skip Muirhead claimed a third European title in her eighth final.
"I never thought I'd do this again," she admitted. "It's been a tough year and I've been through a lot with my hip surgery (in 2018). It's been a bit of a rollercoaster with forming the new team this season, but this result shows that it has worked."
Team Muirhead's next goal is to book their place at February's Winter Olympics in Beijing when they contest next month's final qualifiers in Holland.
"The Olympics is the most important event, so we'll have to put this win to the back of our minds," warned Muirhead.
Mouat and his team-mates Hammy McMillan, Bobby Lammie and Grant Hardie then took to the ice against seven-time European champion Niklas Edin, whose rink beat the Scots in last season's world final in Canada.
Team Mouat gained revenge with an 8-5 victory last night, giving them a perfect record of 11 wins from 11 games this week and clinching their second continental title after also downing Edin in 2018.
"I'm very happy!" beamed Mouat. "What a week we've had. We've put in a lot of hard work, so we're definitely going to enjoy this."We didn't put them under enough pressure at the start, so we all said after the third end that we needed to step it up a bit."