Mouat and Dodds, who were world champions in 2021 and finished in fourth place at the Beijing Olympics in 2022, sit atop the round-robin standings after winning their first seven games in the competition.
They can no longer be caught by Canada or Switzerland, who are joint-fifth.
The British pair sealed a hard-fought win over Canada's Brett Gallant and Jocelyn Peterman in the morning session, before returning to the ice and beating Americans Korey Dropkin and Cory Thiesse 6-4.
"It's always a nice feeling to know you're qualified, but we want to still continue to play well," Dodds said.
"And today, those two games were definitely our A performances out there and we'll need to continue that. So we'll continue that into tomorrow and hopefully we can secure a top spot."
It was a disappointing day for the US, who also suffered a 6-5 defeat to South Korea's Jeong Yeong-seok and Kim Seon-yeong.
Italy beat Norway, again
In the evening session, champions Italy beat two-times Olympic medallists Magnus Nedregotten and Kristin Skaslien of Norway 6-5 in a rematch of the final in Beijing four years ago.
In a close encounter, both teams appeared to struggle to get a read of the ice, with Norway's Nedregotten miscalculating a shot in the final end which enabled Italy's Stefania Constantini and Amos Mosaner to set up a steal and nab the win.
"Sometimes it's the way the game needs to go, a couple of times we have been unlucky, and this time we were lucky, it's always 50-50," Mosaner said.
"Today we had some luck and we take it, to win a championship we need it."
Italy's win moves them up to joint-second in the standings, with Norway in joint-seventh.
Earlier on Saturday, Sweden's Isabella and Rasmus Wranaa clinched a 9-4 win over Italy to boost their hopes of a top-four finish.
The Czech pairing of Julie Zelingrova and Vit Chabicovsky beat South Korea 9-4 to pick up their first win of the tournament.
Teams play nine times in the round-robin stage at the Cortina Olympic Curling Centre, with the semi-finals taking place on Monday and the medal matches scheduled for Tuesday.