In yet another statement of Dutch dominance, Bergsma crossed the line in a new Olympic record time of 12min 44.45sec, ahead of Sven Kramer (12:49.02) and Bob de Jong (13:07.19)
Speed skating powerhouse the Netherlands had already dominated the podiums in the men's 500m, 5,000m and women's 1,500m.
They have now won 19 of 27 medals up for grabs at the Adler Arena, with six gold medals out of nine events so far.
Bergsma, 28, skated in the penultimate pair and had to watch as Kramer, racing with defending champion Lee Seung-Hoon of South Korea, went last.
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"It is a fantastic feeling," said Bergsma. "I knew with my current shape I could do it, but these are the Olympic Games. You have to cope with the pressure and control your nerves.
"I knew with a good race I would win here. I watched Sven Kramer. He held on for a very long time, but finally he broke."
Speaking about his tactics, he added: "I wanted to go fast, but I didn't want to push it too much. I wanted to keep skating. I was able to do that until the end, and that is a fantastic feeling."
"Being satisfied with silver is not my view on top sport. That is not why I train, that is not why I race. I race to win," said Kramer, 27.
"I knew when I started that Jorrit Bergsma set a really fast time, he just did a really good job."
"My race just was not good enough," he added. "I couldn't find the rhythm and I couldn't find the flow. I'm in good shape, but today too many little things were going wrong."
Aged 37, he is also the second oldest male speed skater to win an Olympic medal and the oldest in 86 years.