The 33-year-old Engleder ranked at or near the top through the kneeling, prone and standing positions of the competition for a total score of 458.6, finishing just 0.2 of a point ahead of first-time Olympian Zhang Binbin of China, who mounted a late surge.
Zhang's high-profile compatriot Du Li, the 2008 Olympic champion, took the bronze after battling with Engleder and surpassing her during the standing portion of the competition.
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Engleder, a sport soldier and mother of a young son, had no idea how close it was at the end. Her final shot was a disappointing 9.0 to Zhang's 10.4 but, when she realised she had won, she dropped to her knees in disbelief.
On the podium she spread her arms wide like Rio's famous Christ statue and, when Germany's anthem began playing, her hard-fought win began to sink in.
"First I couldn't believe it and secondly I did not know if I should start to sing, so I started singing," she said.
Zhang, 27, said she was really nervous in her first Olympic final.
"All I told myself was to get this shot right, to get every shot right," Zhang said, adding "I didn't actually think my last shot was good enough."
Engleder, whose previous highest Olympics placing was sixth in this event in London, said it is time to hang up the rifle.
"This is my last Olympic Games and almost the last competition to shoot," she said. "I am old enough for it now. I am almost 34 and my son needs a steady life and my life is not steady."
Asked what she'll be doing next, Engleder responded: "Drinking a beer."
Du, who is 34 and won a silver medal in the 10 metre air rifle here, said it may also be the end of her career after four Olympic Games and four medals.
"Future plans, I do not know," said Du. "I may give up shooting training."
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