Paget,29, becomes just the second rider to win the prestigious event on debut after fellow Kiwi Mark Todd back in 1980.
Paget, riding Clifton Promise, found himself fourth after the dressage event but moved into second place after a perfect cross-country round, with just Jung ahead of him.
Jung, the pre-tournament favourite, appeared set for victory with just one fence remaining in the final showjumping discipline but with the pressure on, he faltered.
With spectators already hailing him as champion, the German Olympic champion’s horse La Biosthetique Sam sent the final fence tumbling to the ground, stunning the crowd and handing a sensational victory to Paget.
“I have lost out at other four-stars with tiny mistakes and came here secretly knowing I could win,” said Paget.
“I was out in the collecting ring with my horse, not watching Michael – like everyone else I assumed he would do it. Then I heard the roar turn to a gasp and thought: ‘S---, it’s me!’
“When I was young, I was watching videos of Badminton, thinking to myself it must be cool to be there. And now I am here.”
Another Kiwi Andrew Nicholson, with Nereo, went clear in showjumping to finish third, but the day undoubtedly belonged to the ever-improving Paget.