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 'be boring' to get the job done and do it again."
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-placed finish in the singles four years ago.
The team event winners are decided by the aggregate of both athletes' times, but there is extra jeopardy in the event 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 events - a factor that some dealt with better than others with the threat of a huge half-second or more penalty for a false start hanging over them.
Italy’s Valentina Margaglio made some unwelcome Olympic history when she was the first to be penalised for a false start. She was in good company, though, as Austrian Janine Flock, who won the women's individual gold on Saturday, did the same.