Ling made his Olympic debut in 2004 at the age of 21, and finished 25th, improving by four places in 2012.
But he took silver at last year's World Championships in Grenada, and an excellent display in Rio gave him victory 13-9 over David Kostelecky.
Fourth time lucky for Germany's Engleder in 50m rifle
Steven Scott takes bronze for GB in double trap, dances with gun to celebrate
Anna Korakaki takes gold in shooting for Greece to bag second medal