Britain, who had already sealed their playoffs berth on Saturday, had a 4-3 lead at the halfway mark but some pinpoint shot-making from Amos Mosaner set up a massive three-pointer for Italy in the sixth end.
Despite the raucous roars of the home fans at the Cortina Olympic Curling Centre, Britain kept their wits about them and racked up four points in the final two ends to see out the win.
Just a few feet over, Americans Korey Dropkin and Cory Thiesse held off 2024 world champions Isabella and Rasmus Wranaa of Sweden to win 8-7.
Sweden took an early lead but Thiesse nailed a three-pointer and moved her team into a 6-4 lead after the fourth end. The Wranaa siblings were able to level at 7-7, but a miss from Isabella gave the US the win.
"We knew that this was our game to win, you know, they're a great team, but we knew we needed to bring our A game and did that today, so really proud of us," Thiesse said.
"We're just thrilled to be here, to be playing in front of this crowd and to be playing in front of our friends and family and people back home watching. We're just trying to enjoy the moment and take it one rock at a time."
Semi-finals set
Switzerland's 6-3 loss to Norway still ensured that both Italy and Sweden would finish in the top four of the standings and move into the semi-finals.
Britain are top with eight wins from nine games, with the US in second, Italy in third and Sweden fourth.
Teams play nine times in the round-robin stage, with the final four matches set to take place on Monday morning. The semi-finals will follow in the evening on Monday and the medal matches are scheduled for Tuesday.
Jocelyn Peterman and Brett Gallant of Canada lost 9-5 to South Korea's Jeong Yeong-seok and Kim Seon-yeong, a fifth straight defeat after they won their first three games.
Canada, the curling capital of the world, won the inaugural mixed doubles competition at the Pyeongchang Games in 2018, but have not won a medal in the format since.