The 29-year-old world record holder scored 34, beating Frenchman Jean Quiquampoix, who took silver with 30.
A tense shoot-off between Quiquampoix and China's Yuehong Li decided the bronze medal.
Cuba's 2012 Olympic champion Leuris Pupo finished fifth after the first series of eliminations.
Germany equal Great Britain's gold medal tally of eight, having won three shooting titles in Rio.
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German policeman Christian Reitz has won the Olympic men's 25m rapid fire pistol title in Rio.