Just hours after her compatriot Roger Federer won a record eighth Wimbledon singles crown, Hingis made it a double celebration for Switzerland on Centre Court.
Top seeded Hingis and Murray, the brother of men's world number one Andy, saw off Finland's Kontinen and Britain's Watson.
"It's not bad for us!" Hingis said of a memorable day for her and Federer.
"I'm really pleased I contacted Jamie before Wimbledon. I'm really happy how we played.
"We knew before the final a British player was going to win the mixed doubles. I'm just happy it was mine."
Hingis, 36, has now amassed six mixed doubles Grand Slam titles, 12 Grand Slam women's doubles crowns and also won five major singles titles, including Wimbledon in 1997.
Murray got his hands on the Wimbledon mixed doubles silverware 10 years after first winning it with Jelena Jankovic.
The 31-year-old also won the Australian and US Open men's doubles titles in 2016.