Gibson and Mason beat Croatia, top seeds Colombia and Italy in the run-up to facing Slovenia's Toja Ellison and Stas Modic in the gold medal showdown, where the Brits held on to win 156-155.
It is the 10th gold medal Great Britain has won in the Archery World Cup – the first medal since 2012 and the first compound victory since 2010.
The gold is Mason's first-ever medal in the Archery World Cup and the 29-year-old was delighted with his team's achievement.
"We've had a lot of bad luck in the mixed team in the last few years, so it's great to get it here, especially in the mixed team event. Hopefully, we can continue to win more going forward," said Mason.
Gibson, who also took a silver with the British women's compound team event, gave credit to her teammate Mason for only missing the middle once in the 16-arrow final.
"He helped me through shots and it was just really good," said Gibson.
"It was very nerve-wracking, but I really enjoyed getting on the stage."
Gibson, along with Susan Corless and Sarah Moon, defeated New Zealand and Germany to book a title showdown with Turkey, but they were edged 232-221 in the final battle in Berlin and took home silver.
Mason added: "Two medals, which is something the compounds haven't achieved in some time, is fantastic."