Edin struggled to find his range as world champions Britain clinched their second win of the round-robin stage, after beating China in their opener on Wednesday.
"Very consistent from us," Mouat said. "We were pretty relentless and made them play some pretty tricky shots to get into the game. So it's exactly what we wanted to do after a really good performance last night against China."
Mouat and Edin have crossed paths many times before, with the Scot winning 8-4 at the Players' Championship in January, while the Swede took an 8-5 victory in the semi-finals of the European Curling Championships in November.
"Niklas is probably one of the best players that we've ever had in our sport," Mouat said. "We know that we'd have to play well to beat them. His team are just incredible."
Yannick Schwaller's Switzerland beat the United States 8-3, a game in which American curler Rich Ruohonen became the nation's oldest-ever Winter Olympian at 54.
Marc Muskatewitz's Germany, the 2024 European champions, were pushed until the final end by Norway before winning 5-4.
Earlier on Thursday, Canada's bid for a first women's Olympic gold since 2014 began with a commanding 10-4 win over Denmark in their opening round-robin match as the women's curling competition kicked off.
Beijing bronze medallists Sweden, led by Anna Hasselborg, scored an 8-4 victory over Japan while Silvana Tirinzoni's Switzerland beat hosts Italy 7-4 and the US clinched an 8-4 victory over South Korea.
Teams play nine matches in the round-robin stage, which continues on Thursday. The top four advance to the semi-finals next week.