Propelled by a deafening roar inside London's Aquatic Centre, Gyurta held on to beat Jamieson in a desperate finish to win in a time of two minutes 07.28 seconds.
Gyurta shaved 0.03 off the previous world record set by Australia's Christian Sprenger at the 2009 world championships in Rome when the now-banned polyurethane bodysuits were still allowed.
Scot Jamieson was second in 2:07.43 after almost drawing level with Gyurta approaching the wall while Japan's Ryo Tateishi, swimming in the outside lane, was third in 2:08.29.
His countryman Kosuke Kitajima, the two-time defending champion, finished fourth, dashing his hopes of becoming the first male swimmer to win the same event at three successive Olympics.
Jamieson produced a remarkable last 50m for silver and the Glasgow swimmer was delighted to get second with a well-executed plan but insisted he had prepared for this moment all his life.
“I planned for this night and I think that has helped,” said the Bath-based Jamieson.
“I’ve gone over this for so many years in my head and how I was going to prepare for it. I can’t believe it – I’m so delighted.
“To be honest, tonight wasn’t about the times for me. I know how strong Gyurta’s first 100m – he’s the fastest in the world without a doubt.
“I tried to stay on his shoulder for the first hundred and the idea was to make a move on the second 25 and the last 50. I just put everything on the line in the last 50m.”
Jamieson paid tribute to all the support he’s received before the race, including his family who were present at the pool to watch his achievement, and also predicted big things for Andrew Willis, who came eighth.
He said: “I loved it. It’s so much easier to swim with a bit of confidence behind me, like I did after the 100m and a few rounds here.
“I’ve had so many messages – it’s unbelievable and I was desperate to get on the podium to repay the faith.
“My family are here and it’s great they can share it. It’s great to have them here and their support.
“Andy is going to be tough to beat over the next few years. Some of the swimming he’s had over the years has been unbelievable and seeing him training, it’s pretty frightening.
“He’s definitely going to be the man to beat in few years.”
Willis, who finished in a time of 2:09.44 mins, believes he left it all in the pool and returned the compliment to Jamieson.
He said: “It was a tough race and I gave it my all. I’m really happy for Michael and he deserves it a 100 percent. It was great for me to experience it as well.”
Three-time Olympian Gyurta had won silver in the 200 in Athens in 2004 at just 15, but then slipped to fifth in Beijing.
He has since bounced back with a storming four years, winning the last two European and two world championships.
"I managed to prove to everyone and to myself after those devastating two years after the 2004 Olympic Games that I could bounce back, and do what I dreamed of since my childhood," said the visibly elated 23-year-old. "It is the biggest achievement of my life."
In a race that pitted some of the greatest names in the stroke against newer arrivals, Gyurta shaved 0.03 off the record set by Australia's Christian Sprenger at the 2009 world championships, when the now-banned bodysuits were still allowed.
Kitajima, hugely popular in Japan, has dominated breaststroke since the 2003 world championships in Barcelona. He went on to win the breaststroke double at Athens in 2004 and Beijing four years later.
In London he had been locked in a race with Michael Phelps to become the first male swimmer to do the three-peat.
When Phelps failed to win a medal in the 400 medley on Saturday, Kitajima got the opportunity to become the first, but he missed the podium altogether in his own first event, the 100 breaststroke, only to miss it again in his second.
Phelps has two more opportunities this week, with the 100 fly and the 200 individual medley.
"I swam my own race," Kitajima said. "I have no regrets."
1. Daniel Gyurta (Hungary) 2:07.28
2. Michael Jamieson (Britain) 2:07.43
3. Ryo Tateishi (Japan) 2:08.29
4. Kosuke Kitajima (Japan) 2:08.35
5. Scott Weltz (U.S.) 2:09.02
6. Clark Burckle (U.S.) 2:09.25
7. Brenton Rickard (Australia) 2:09.28
8. Andrew Willis (Britain) 2:09.44
- Kosuke Kitajima
- Christian Sprenger