The 33-year-old mother of two, who claimed back-to-back sprint titles in the 7.5km event at Vancouver and Sochi, became the first woman to clinch biathlete golds in three successive Games, winning with a time of 35 minutes 23 seconds.
Belarusian triple Olympic champion Darya Domracheva grabbed silver, 18.8 seconds behind Kuzmina, while Norway's Tiril Eckhoff took bronze.
"I expected to have the best chance in the gold medal for sprint here," Kuzmina told reporters.
"When this didn’t happen I was really sad and nervous before the next races. But it happened here ... A different event from Vancouver and Sochi, so it’s an incredible feeling."
With the 30 athletes split into 10 groups of three, Kuzmina started in the second row, battling for position all the way to the first shoot.
Her accuracy on the range laid the foundation for her victory, but despite showing nerves of steel on a chilly night, eventually even she got rattled.
Having built up a considerable lead, Kuzmina arrived at the fourth shoot and made her first four shots before taking a very long pause and then missing her final effort as the rest of the field skied in towards the range.
"In my career I never shoot clean four times, and today after three times zero, I was reaching for my last shooting, and I was worried about it," she said.
"I'm so happy that my ski time was good enough, and saved my position."
The miss meant she was diverted to ski a 150-metre penalty lap, but she remained in the lead and surged away to the finish, waving a Slovakian flag proudly as she crossed the line.
Germany's Laura Dahlmeier, who started the Games with golds in the sprint and pursuit races, struggled with the rifle, missing once in each of her first two shoots before finishing a disappointing 16th.
Kuzmina's triumph equalled the Slovakian record held by twin brothers in canoe slalom, Pavol and Peter Hochschorner, of three gold medals at Summer and Winter Games.
"The first medal was conquered for me, the second was for my brother because I was sad that he was missing (from) here," said Kuzmina.
"He was supporting me (from home) like he was able.
"Now this third medal is for the entire Slovakia, for my team and for the many people who were supporting me through the hard times."
(Additional reporting by Ian Ransom; Editing by Clare Fallon and Clare Lovell)
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