Germans Axel Jungk and Susanne Kreher, who both got silver in the singles, edged out compatriots Christopher Grotheer and Jacqueline Pfeifer, who both got singles bronze, by 100th of a second in the battle for the minor medals.
It was another incredible performance by Weston, who found himself in fourth place, three-tenths adrift, after Stoecker lost time on the bottom stages of the run. But showing the skill and calmness that has brought him three successive World Cup titles and a first men’s Olympic skeleton gold for Britain, he blasted off at his start to make up the deficit almost immediately and then found the perfect line to win by 0.17 seconds.
"Luckily, I felt like I knew what I needed to do," Weston said. "I took a load of confidence from the individual event, and I almost had to say to myself, 'Be boring and just get the job done.
"It was probably my best run of the five, between the individuals. The individual event is amazing, and I’m very pleased with that, but doing it as a team in an individual sport, and to have my teammate by my side, being Olympic champions, and for me two times, is absolutely mental."
Stoecker, who finished fifth in the individual event, must have thought she had blown it when she climbed off her sled to see a 'four' next to her name, but Weston came to the rescue.
"Thanks," she said. "I can't believe it. It's a team effort, and when Matt came down, and we were in the green, I was just in shock."
Britain topped the World Cup rankings with Marcus Wyatt and Stoecker together, but opted on Sunday to break that team up and reprise the pairing that finished second in the last two world championships.
It proved an inspired decision as Weston became the first Briton to win two medals at a Winter Olympics, capping an amazing week after the disappointment of his 15th-place finish in the singles four years ago.
Wyatt finished fourth with Freya Tarbit.
The mixed team gold medal further cemented Britain’s position as the most successful skeleton nation in Olympic history, despite not having a track in the country.
It also means they have won three titles in a single Winter Games for the first time after Charlotte Bankes and Huw Nightingale won the Mixed Snowboard Cross earlier on Sunday.
The team event is decided by the aggregate of both athletes' times, but there is extra jeopardy as they each have to wait for a green signal from a light display rather than automatically starting the clock when they cross a beam as in singles, with the threat of huge time penalties for a false start.
Italy’s Valentina Margaglio made some unwelcome Olympic history when she was the first to be penalised for going too early, but she was in good company as Austrian Janine Flock, who won the women's individual gold on Saturday, did the same.
One spectator was International Olympic Committee President Kirsty Coventry, whose last visit to the Sliding Centre was to tearfully confirm the disqualification of Ukrainian Vladyslav Heraskevych over his "helmet of remembrance."