Kim finished on 792.4 points, beating defending champion Chen Ying of China by one point, and falling one point short of the Olympic finals record, which Chen set four years ago in Beijing.
"This medal is really heavy," Kim said through an interpreter, while lifting the medal carefully with both hands. "Every shot was a pressure one."
Olena Kostevych of Ukraine won her second bronze medal after placing third in the 10M air pistol Sunday.
With her impressive performance, Kim confirmed her status as the rising star of women's shooting.
In qualification, she scored 591 points to beat the 12-year-old previous mark by one point. Kim scored 298 points in the precision stage before adding 293 in the rapid stage to break the record set by Tao Luna of China at the 2000 Sydney Games.
The 1.60-meter tall Kim started shooting seven years ago. She is the Youth Olympic Games champion and dominated the London World Cup in April on the same Royal Artillery Barracks range. The 19-year-old Kim beat the field by five points with a world record at the World Cup.
She carried a six-point lead over Chen into the final, but the Chinese narrowed the gap with every round. Before the final five shots, she even held a 0.8-point lead over Kim, who showed her class to get back in front again.
"I would not have been able to sleep tonight if I had lost the final by such a small margin," Kim said. "Now I will celebrate with the whole team. I'll pay for the diner."
Kim said her title proves that South Korean women can shoot as well as their male counterparts.
"The men do usually very good," she said. "The last gold for a South Korean woman was 20 years ago, so I am glad I could show today that women are equally competitive with men in this sport."
Chen said taking the lead before the last round did not make her nervous.
"No, I think I have performed as well as I could," Chen said. "I am happy with the silver medal."
Chen just missed out on winning China a third gold in women's shooting, after teammates Yi Siling won the 10-meter air rifle and Guo Wenjun successfully defend her 10-meter air pistol title.
Title favourite Lenka Maruskova of the Czech Republic failed to qualify for the final. She won silver in Athens in 2004, but also lost in qualification four years later in Beijing. She was on the podium of all three World Cup events so far this year.
After three competitors shared seventh after qualification, Jo Yong Suk of North Korea and Zorana Arunovic of Serbia won the shoot-off, denying Maria Grozdeva of Bulgaria a spot in the final and a chance of a third Olympic victory. Grozdeva won the 25-meter pistol title in 2000 and 2004.